قراءات إضافية | الدرجات الست وأسرار الشبكات: علم لعصر متشابك

درجات الصعوبة

⋆ Beginner (no more difficult than this book).
⋆⋆ Intermediate (some effort and mathematical background required).
• Advanced (requires undergraduate-level mathematics training).
•• Expert (impenetrable without graduate-level mathematics training).

الفصل الأول: عصرنا المتشابك

The proximate causes and immediate effects of the cascading failure that occurred in the Western Systems Coordinating Council transmission grid on August 10, 1996, are described in:

⋆ WSCC Operations Committee. Western Systems Coordinating Council Disturbance Report, August 10, 1996 (October 18, 1996). Available on-line at http://www.wscc.com/outages.htm.
A review of major recent power disturbances in the United States that sheds some additional light on the August 10 cascade is:

⋆ Hauer, J. F., and Dagel, J. E. White Paper on Review of Recent Reliability Issues and System Events. Consortium for Electric Reliability Technology Solutions. U.S. Department of Energy (1999). Available on-line at http://www.eren.doe.gov/der/transmission/pdfs/reliabilityevents.pdf.
Some theoretical papers dealing with the problem of cascading failures in power transmission networks are:

⋆⋆ Kosterev, D. N., Taylor, C. W., and Mittelstadt, W. A. Model validation for the August 10, 1996 WSCC system outage. IEEE Transactions on Power Systems, 14(3), 967–979 (1999).

• Sachtjen, M. L., Carreras, B. A., and Lynch, V. E. Disturbances in a power transmission system. Physical Review E, 61(5), 4877–4882 (2000).

•• Asavathiratham, C. The influence model: A tractable representation for the dynamics of networked Markov chains (Ph.D. dissertation, Department of Electrical Engineering and Computer Science, MIT, 2000).

(١) النشوء

Although the author doesn’t call it emergence, one of the earliest works to really grapple with the issue of emergent behavior in complex (social) systems is:

⋆ Schelling, T. C. Micromotives and Macrobehavior (Norton, New York, 1978).
The classic paper by Phillip Anderson that outlines the fundamental concept of emergence is:

⋆⋆ Anderson, P. W. More is different. Science, 177, 393–396 (1972).
Some very readable introductions to the subject of complex, adaptive systems in general, and emergence in particular, are:

⋆ Gell-Mann, M. The Quark and the Jaguar: Adventures in the Simple and the Complex (W. H. Freeman, New York, 1994).

⋆ Holland, J. H. Hidden Order: How Adaptation Builds Complexity (Perseus, Cambridge, MA, 1996).

⋆ Waldrop, M. M. Complexity: The Emerging Science at the Edge of Order and Chaos (Touchstone, New York, 1992).
A more technical read is:

• Casti, J. L. Reality Rules I & II: Picturing the World in Mathematics: The Fundamentals, the Frontier (Wiley-Interscience, New York, 1997).

(٢) الشبكات

A good introduction to the mathematical theory of graphs (and one that explains Euler’s theorem in detail) is:

⋆⋆ West, D. B. Introduction to Graph Theory (Prentice-Hall, Upper Saddle River, NJ, 1996).
A more applied approach to the subject, focusing more on algorithms and applications than on theorems, is presented in the following general texts:

⋆⋆ Lynch, N. A. Distributed Algorithms (Morgan Kauffman, San Francisco, 1997).

⋆⋆ Ahuja, R. K., Magnanti, T. L., and Orlin, J. B. Network Flows: Theory, Algorithms, and Applications (Prentice-Hall, Englewood Cliffs, NJ, 1993).

•• Nagurney, A. Network Economics: A Variational Inequality Approach (Kluwer Academic, Boston, 1993).

(٣) المزامنة

The best way to learn about the subject of coupled oscillators is from Steve Strogatz himself in his recent book:

⋆ Strogatz, S. H. Sync: The Emerging Science of Spontaneous Order (Hyperion, Los Angeles, 2003).
Strogatz has also written two shorter accounts of his (and related) work on the Kuramoto model:

• Strogatz, S. H. Norbert Wiener’s brain waves. In Levin, S. A. (ed.), Frontiers in Mathematical Biology, Lecture Notes in Biomathematics, 100 (Springer, New York, 1994), pp. 122–138.

⋆ Strogatz, S. H., and Stewart, I. Coupled oscillators and biological synchronization. Scientific American, 269(6), 102–109 (1993).

(٤) الطريق الأقل ارتيادًا

Winfree’s original paper on the entrainment of coupled oscillators that kicked off much of the recent literature, and that was my initial reference point, is:

• Winfree, A. T. Biological rhythms and the behavior of populations of coupled oscillators. Journal of Theoretical Biology, 16, 15–42 (1967).
For those who want to learn more from the master, a fascinating (albeit a somewhat challenging) read is:

• Winfree, A. T. The Geometry of Biological Time (Springer, Berlin, 1990).

(٥) مسألة العالم الصغير

The famous Psychology Today paper that everyone cites when they talk about Milgram’s work is:

⋆ Milgram, S. The small world problem. Psychology Today, 2, 60–67 (1967).
A better reference, however, is a paper that Milgram published two years later with his graduate student, Jeffrey Travers. It contains considerably more detail than the Psychology Today article, and although it isn’t quite as fun, it is actually much clearer.

⋆ Travers, J., and Milgram, S. An experimental study of the small world problem. Sociometry, 32(4), 425–443 (1969).
The very first study of the small-world problem was by Manfred Kochen and Ithiel de Sola Pool, who circulated their results as a working paper almost ten years before Milgram conducted his experiment. In fact, it was this paper that stimulated Milgram’s work in the first place. It was finally published, almost twenty years after its inception, as the first paper in the first volume of the journal Social Networks.

⋆⋆ Pool, I. de Sola, and Kochen, M. Contacts and influence. Social Networks, 1(1), 1–51 (1978).
A number of subsequent papers, both theoretical and empirical, as well as the original paper by Kochen and Pool, are available in a collected volume, edited by Manfred Kochen.

⋆⋆ Kochen, M. (ed.). The Small World (Ablex, Norwood, NJ, 1989).
The play by John Guare that was later made into a movie, and launched the phrase “six degrees of separation” into the pop-culture stratosphere, is:

⋆ Guare, J. Six Degrees of Separation: A Play (Vintage Books, New York, 1990).

الفصل الثاني: أصول علم «جديد»

(١) نظرية الرسوم البيانية العشوائية

Random-graph theory is not for the faint of heart. As a result, there are not really any readings one might call “accessible.” Nevertheless, here are some important ones. The original results of Erdős and Rényi dealing with the evolution and connectedness of random graphs are contained in the following series of classic papers (none of which are easy to find in your average library):

•• Erdős, P., and Rényi, A. On random graphs. Publicationes Mathematicae, 6, 290–297 (1959).

•• Erdős, P., and Rényi, A. On the evolution of random graphs. Publications of the Mathematical Institute of the Hungarian Academy of Sciences, 5, 17–61 (1960).

•• Erdős, P., and Rényi, A. On the strength and connectedness of a random graph. Acta Mathematica Scientia Hungary, 12, 261–267 (1961).
The standard textbook for the field of random graphs, and one that summarizes the most significant developments since Erdős and Rényi, is:

•• Bollobas, B. Random Graphs, 2d ed. (Academic, New York, 2001).
A slightly more readable (although not as comprehensive) treatment of the subject is:

• Alon, N., and Spencer, J. H. The Probabilistic Method (Wiley-Interscience, New York, 1992).

(٢) الشبكات الاجتماعية

The standard textbook for social network analysis is:

⋆⋆ Wasserman, S., and Faust, K. Social Network Analysis: Methods and Applications (Cambridge University Press, Cambridge, 1994).
Two shorter, less comprehensive, but more readable alternatives are:

⋆⋆ Degenne, A., and Forse, M. Introducing Social Networks (Sage, London, 1999).

⋆⋆ Scott, A. Social Network Analysis, 2d ed. (Sage, London, 2000).
Finally, a very short collection of classic papers—the ones that introduced some of the central concepts in the field—includes:

⋆⋆ Boorman, S. A., and White, H. C. Social structure from multiple networks. II. Role structures. American Journal of Sociology, 81(6), 1384–1446 (1976).

⋆⋆ Burt, R. S. Structural Holes: The Social Structure of Competition (Harvard University Press, Cambridge, MA, 1992).

⋆⋆ Davis, J. A. Structural balance, mechanical solidarity, and interpersonal relations. American Journal of Sociology, 68(4), 444–462 (1963).

⋆⋆ Freeman, L. C. A set of measures of centrality based on betweenness. Sociometry, 40, 35–41 (1977).

⋆⋆ Granovetter, M. S. The strength of weak ties. American Journal of Sociology, 78, 1360–1380 (1973).

⋆⋆ Harary, F. Graph theoretic measures in the management sciences. Management Science, 5, 387–403 (1959).

•• Holland, P. W., and Leinhardt, S. An exponential family of probability distributions for directed graphs. Journal of the American Statistical Association, 76, 33–65 (1981).

⋆⋆ Lorrain, F., and White, H. C. Structural equivalence of individuals in social networks. Journal of Mathematical Sociology, 1, 49–80 (1971).

•• Pattison, P. Algebraic Models for Social Networks (Cambridge University Press, Cambridge, 1993).

⋆⋆ White, H. C., Boorman, S. A., and Breiger, R. L. Social structure from multiple networks. I. Blockmodels of roles and positions. American Journal of Sociology, 81(4), 730–780 (1976).

(٣) للديناميكيات أهمية

Because the subject of networks and dynamics is such a new one, there is really no text on the subject. One starting place is the following edited volume—a collection of roughly forty papers with introductions written by the editors:

•• Newman, M. E. J., Barabási, A. L., and Watts, D. J. The Structure and Dynamics of Networks (Princeton University Press, Princeton, NJ, 2003).
A great introduction to the field of nonlinear dynamics is:

⋆⋆ Strogatz, S. H. Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry, and Engineering (Addison-Wesley, Reading, MA, 1994).
And a discussion of its relevance to networks is:

⋆⋆ Strogatz, S. H. Exploring complex networks. Nature, 410, 268–275 (2001).
A paper that points out the limitations of centrality as a surrogate for social influence is:

⋆⋆ Mizruchi, M. S., and Potts, B. B. Centrality and power revisited: Actor success in group decision making. Social Networks, 20, 353–387 (1998).
The story quoting Jon Kleinberg on the connection to Bill Gates is:

⋆ Wildavsky, B. Small world, isn’t it? U.S. News and World Report, April 1, 2002, p. 68.
And the article that suggested OTPOR as a good example of decentralized action is:

⋆ Cohen, R. Who really brought down Milosevic? New York Times Magazine, November 26, 2000, p. 43.

(٤) الابتعاد عن العشوائية

Over a period of more than a decade, Anatol Rapoport produced a series of papers that laid out the theory of random-biased nets. The central ideas, however, are contained in the following pair of papers:

• Solomonoff, R., and Rapoport, A. Connectivity of random nets. Bulletin of Mathematical Biophysics, 13, 107–117 (1951).

• Rapoport, A. A contribution to the theory of random and biased nets. Bulletin of Mathematical Biophysics, 19, 257–271 (1957).
A summary of the random-biased network approach is given in:

• Rapoport, A. Mathematical models of social interaction. In Luce, R. D., Bush, R. R., and Galanter, E. (eds.), Handbook of Mathematical Psychology, vol. 2 (Wiley, New York, 1963), pp. 493–579.
Rapoport’s own account of his life, and his life’s work, is:

⋆ Rapoport, A. Certainties and Doubts: A Philosophy of Life (Black Rose Press, Montreal, 2000).

(٥) دور الفيزيائيين

The classic text on the theory of critical phenomena is:

• Stanley, H. E. Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, Oxford, 1971).
A more contemporary version is:

• Sornette, D. Critical Phenomena in Natural Sciences (Springer, Berlin, 2000).
A detailed discussion of spin systems and phase transitions is given in:

• Palmer, R. Broken ergodicity. In Stein, D. L. (ed.), Lectures in the Sciences of Complexity, vol. I, Santa Fe Institute Studies in the Sciences of Complexity (Addison-Wesley, Reading, MA, 1989), pp. 275–300.

• Stein, D. L. Disordered systems: Mostly spin systems. In Stein, D. L. (ed.), Lectures in the Sciences of Complexity, vol. I, Santa Fe Institute Studies in the Sciences of Complexity (Addison-Wesley, Reading, MA, 1989), pp. 301–354.
If one actually wants to do work in this field, a useful text is:

• Newman, M. E. J., and Barkema, G. T. Monte Carlo Methods for Statistical Physics (Clarendon Press, Oxford, 1999).
And finally, a very accessible text that uses simple computer models to explain many of the central concepts of nonlinear dynamics and critical phenomena is:

⋆⋆ Flake, G. W. The Computational Beauty of Nature: Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptation (MIT Press, Cambridge, MA, 1998).

الفصل الثالث: عوالم صغيرة

The original account of my work with Steve Strogatz was my Ph.D. dissertation, later published as:

⋆⋆ Watts, D. J. Small Worlds: The Dynamics of Networks between Order and Randomness (Princeton University Press, Princeton, NJ, 1999).

(١) مساعدة بسيطة من الأصدقاء

A discussion of agency, as the term is understood by sociologists, is:

⋆ Emirbayer, M., and Mische, A. What is agency? American Journal of Sociology, 103(4), 962–1023 (1998).
The computer algorithms used to do the relevant calculations are quite standard and can be learned from any good text on algorithms. Two good examples are:

⋆⋆ Aho, A. V., Hopcroft, J. E., and Ullman, J. D. Data Structures and Algorithms (Addison-Wesley, Reading, MA, 1983).

⋆⋆ Ahuja, R. K., Magnanti, T. L., and Orlin, J. B. Network Flows: Theory, Algorithms, and Applications (Prentice-Hall, Englewood Cliffs, NJ, 1993).

(٢) من سكان الكهوف إلى أهالي سولاريا

The two books from Asimov’s Robot series that inspired my discussion with Steve are:

⋆ Asimov, I. The Caves of Steel (Doubleday, Garden City, NY, 1954).

⋆ Asimov, I. The Naked Sun (Doubleday, Garden City, NY, 1957).

(٣) عوالم صغيرة

The derivation of the alpha model, and the consequent identification of small-world networks, are presented in:

⋆⋆ Watts, D. J. Networks, dynamics and the small-world phenomenon. American Journal of Sociology, 105(2), 493–527 (1999).
A simpler, but similar, version of the model was later studied by:

• Jin, E. M., Girvan, M., and Newman, M. E. J. The structure of growing networks. Physical Review E, 64, 046132 (2001).

(٤) بسيط قدر المستطاع

The beta model and the empirical results about small-world networks were first published in:

⋆⋆ Watts, D. J., and Strogatz, S. H. Collective dynamics of ‘small-world’ networks. Nature, 393, 440–442 (1998).
Subsequent work on the beta model, and even simpler related models, includes:

• Barthelemy, M., and Amaral, L. A. N. Small-world networks: Evidence for a crossover picture. Physical Review Letters, 82, 3180–3183 (1999).

•• Monasson, R. Diffusion, localization and dispersion relations on ‘small-world’ lattices. European Physical Journal B, 12(4), 555–567 (1999).

• Newman, M. E. J., and Watts, D. J. Scaling and percolation in the small-world network model. Physical Review E, 60, 7332–7342 (1999).

• Newman, M. E. J., and Watts, D. J. Renormalization group analysis of the small-world network model. Physics Letters A, 263, 341–346 (1999).

• Newman, M. E. J., Moore, C., and Watts, D. J. Mean-field solution of the small-world network model. Physical Review Letters, 84, 3201–3204 (2000).
Much of this early work is reviewed in:

• Newman, M. E. J. Models of the small world. Journal of Statistical Physics, 101, 819–841 (2000).

(٥) العالم الواقعي

In addition to exploring the theoretical properties of small-world networks, researchers have identified a wide variety of empirical cases. Some examples are:

⋆⋆ Adamic, L. A. The small world web. In Lecture Notes in Computer Science, 1696, Proceedings of the European Conference in Digital Libraries (ECDL) ’99 Conference (Springer, Berlin, 1999), pp. 443–454.

⋆ Davis, G. F., Yoo, M., and Baker, W. E. The small world of corporate elite (working paper, University of Michigan Business School, 2002).

⋆⋆ Ferrer i Cancho, R., Janssen, C., and Solé, R. V. Topology of technology graphs: Small world patterns in electronic circuits. Physical Review E, 64, 046119 (2001).

⋆ Kogut, B., and Walker, G. The small world of Germany and the durability of national networks. American Sociological Review, 66(3), 317–335 (2001).

⋆⋆ Sporns, O., Tononi, G., and Edelman, G. M. Theoretical neuroanatomy: Relating anatomical and functional connectivity in graphs and cortical connection matrices. Cerebral Cortex, 10, 127–141 (2000).

⋆⋆ Wagner, A., and Fell, D. The small world inside large metabolic networks. Proceedings of the Royal Society of London, Series B, 268, 1803–1810 (2001).

الفصل الرابع: ما وراء العالم الصغير

(١) الشبكات عديمة المعيار

A highly accessible account of the science of networks that focuses on the development and importance of scale-free networks is:

⋆ Barabási, A. L. Linked: The New Science of Networks (Perseus Press, Cambridge, MA, 2002).
Some more mathematical treatments of random networks with non-Poisson degree distributions (including power-law distributions) can be found in:

•• Aiello, W., Chung, F., and Lu, L. A random graph model for massive graphs. In Proceedings of the 32nd Annual ACM Symposium on the Theory of Computing (Association for Computing Machinery, New York, 2000), pp. 171–180.

•• Molloy, M., and Reed, B. A critical point for random graphs with a given degree sequence. Random Structures and Algorithms, 6, 161–179 (1995).

•• Molloy, M., and Reed, B. The size of the giant component of a random graph with a given degree sequence. Combinatorics, Probability, and Computing, 7, 295–305 (1998).

•• Newman, M. E. J., Strogatz, S. H., and Watts, D. J. Random graphs with arbitrary degree distributions and their applications. Physical Review E, 64, 026118 (2001).

(٢) الأثرياء يزدادون ثراء

The paper by László Barabási and Réka Albert that introduced the idea of scale-free networks, and proposed a preferential attachment model of network growth to account for them, is:

⋆⋆ Barabási, A., and Albert, R. Emergence of scaling in random networks. Science, 286, 509–512 (1999).
Since Barabási and Albert’s original paper, a great many papers have been written on the subject of scale-free networks. Many of the references and relevant results are summarized in:

• Albert, R., and Barabási, A. L. Statistical mechanics of complex networks. Review of Modern Physics, 74, 47–97 (2002).
Oddly enough, the original discovery of scale-free networks predates László Barabási and Réka Albert’s paper by over thirty years. The empirical observation that networks can have a power-law degree distribution was first presented by Derek de Solla Price in:

⋆⋆ Price, D. J. de Solla. Networks of scientific papers. Science, 149, 510–515 (1965).
Eleven years later, Price proposed a mathematical model that was, in essence, identical to that of Barabási and Albert’s. Given how popular the notion of scale-free networks has become, one might wonder why no one picked up on it at the time. Perhaps the title (and the journal) had something to do with it.

⋆⋆ Price, D. J. de Solla. A general theory of bibliometrics and other cumulative advantage processes. Journal of the American Society of Information Science, 27, 292–306 (1976).
Continuing on an historical note, Zipf’s law was first proposed in:

⋆⋆ Zipf, G. K. Human Behavior and the Principle of Least Effort (Addison-Wesley, Cambridge, MA, 1949).
And Herbert Simon first presented the idea of preferential, random growth as an explanation of power-law size distributions like Zipf’s law in:

• Simon, H. A. On a class of skew distribution functions. Biometrika, 42, 425–440 (1955).
The article was reprinted two decades later, along with a significant amount of subsequent and related work, in:

• Ijiri, Y., and Simon, H. A. Skew Distributions and the Sizes of Business Firms (Elsevier/North-Holland, New York, 1977).
Finally, the notion of the Matthew effect in the context of scientific prestige was introduced by Robert K. Merton in:

⋆ Merton, R. K. The Matthew effect in science. Science, 159, 56–63 (1968).

(٣) تحقيق الثراء يمكن أن يكون عسيرًا

Empirical evidence (mostly) for and (occasionally) against the prevalence of scale-free networks has appeared in a number of places. Some of the more interesting papers are as follows:

⋆⋆ Amaral, L. A. N., Scala, A., Barthelemy, M., and Stanley, H. E. Classes of behavior of small-world networks. Proceedings of the National Academy of Sciences, 97, 11149–11152 (2000).

⋆⋆ Adamic, L. A., and Huberman, B. A. Power-law distribution of the World Wide Web. Science, 287, 2115a (2000).

⋆⋆ Barabási, A. L., Albert, R., Jeong, H., and Bianconi, G. Power-law distribution of the World Wide Web, Science, 287, 2115b (2000).

⋆⋆ Faloutsos, M., Faloutsos, P., and Faloutsos, C. On power-law relationships of the Internet topology. Computer Communication Review, 29, 251–262 (1999).

⋆⋆ Liljeros, F., Edling, C. R., Amaral, L. A. N., Stanley, H. E., and Aberg, Y. The web of human sexual contacts. Nature, 411, 907–908 (2001).

• Rapoport, A. Mathematical models of social interaction. In Luce, R. D., Bush, R. R., and Galanter, E. (eds.), Handbook of Mathematical Psychology, Vol. 2 (Wiley, New York, 1963), pp. 493–579.

⋆⋆ Redner, S. How popular is your paper? An empirical study of the citation distribution. Europhysics Journal B, 4, 131–134 (1998).

(٤) إعادة تقديم بنية المجموعات

The paper Harrison presented that triggered our work on affiliation networks is:

⋆ White, H. C. What is the center of the small world? (paper presented at American Association for the Advancement of Science annual symposium, Washington, D.C., February 17–22, 2000).
And two classic references dealing with the importance of groups to the structure of social networks are:

⋆⋆ Nadel, F. S. Theory of Social Structure (Free Press, Glencoe, IL, 1957).

⋆⋆ Breiger, R. L. The duality of persons and groups. Social Forces, 53, 181–190 (1974).

(٥) شبكات الارتباط

A good basic reference for affiliation networks is:

⋆⋆ Wasserman, S., and Faust, K. Social Network Analysis: Methods and Applications (Cambridge University Press, Cambridge, 1994).

(٦) المديرون والعلماء

Jerry Davis’s work on interlocking boards of corporate directors is presented in:

⋆ Davis, G. F. The significance of board interlocks for corporate governance. Corporate Governance, 4(3), 154–159 (1996).

⋆ Davis, G. F., and Greve, H. R. Corporate elite networks and governance changes in the 1980s. American Journal of Sociology, 103(1), 1–37 (1997).
And Mark Newman’s data on collaboration networks of scientists is:

⋆⋆ Newman, M. E. J. The structure of scientific collaboration networks. Proceedings of the National Academy of Sciences, 98, 404–409 (2001).
Or in (slightly exhausting) detail:

⋆⋆ Newman, M. E. J. Scientific collaboration networks: I. Network construction and fundamental results. Physical Review E, 64, 016131 (2001).

⋆⋆ Newman, M. E. J. Scientific collaboration networks: II. Shortest paths, weighted networks, and centrality. Physical Review E, 64, 016132 (2001).

(٧) تعقيدات

The mathematical machinery used to analyze the affiliation networks is described in:

•• Newman, M. E. J., Strogatz, S. H., and Watts, D. J. Random graphs with arbitrary degree distributions and their applications. Physical Review E, 64, 026118 (2001).
And a slightly more readable version is:

• Newman, M. E. J., Watts, D. J., and Strogatz, S. H. Random graph models of social networks. Proceedings of the National Academy of Sciences, 99, 2566–2572 (2002).

الفصل الخامس: البحث في الشبكات

A compendium of Milgram’s research over his entire, fascinating career is:

⋆ Milgram, S. The Individual in a Social World: Essays and Experiments, 2d ed. (McGraw-Hill, New York, 1992).
A detailed description of his obedience experiments is in:

⋆ Milgram, S. Obedience to Authority: An Experimental View (Harper & Row, New York, 1974).

(١) ما الذي أوضحه ميلجرام حقًّا؟

Judith Kleinfeld’s paper that exams the history and empirical validity of the small-world problem is:

⋆ Kleinfeld, J. S. The small world problem. Society, 39(2), 61–66 (2002).
The most significant follow-up study to the original experiment is one that Milgram conducted with another student, Charles Korte, in which they attempted to connect a white population of senders in Los Angeles with white and African-American targets in New York:

⋆ Korte, C., and Milgram, S. Acquaintance networks between racial groups—application of the small world method. Journal of Personality and Social Psychology, 15(2), 101 (1970).

(٢) هل الرقم ستة كبير أم صغير؟

The problem of Erdős numbers has been studied extensively by the mathematician Jerry Grossman, who maintains a Web page on the subject at http://www.oakland.edu/~grossman/erdoshp.html. An early summary of his work is:

⋆⋆ Grossman, J. W., and Ion, P. D. F. On a portion of the well-known collaboration graph. Congressus Numerantium, 108, 129–131 (1995).
Some more recent work on Erdős numbers is by:

⋆⋆ Batagelj, V., and Mrvar, A. Some analyses of Erdős collaboration graph. Social Networks, 22(2), 173–186 (2000).
Other evidence that small-world networks can make problem-solving harder, rather than easier, is presented in:

• Walsh, T. Search in a small world. In Proceedings of the 16th International Joint Conference on Artificial Intelligence (Morgan Kaufmann, San Francisco 1999), pp. 1172–1177.

(٣) مشكلة البحث في مسألة العالم الصغير

Jon Kleinberg’s groundbreaking paper, which pointed out and then solved the small-world search problem, is available in two versions, long and short, respectively:

• Kleinberg, J. The small-world phenomenon: An algorithmic perspective. In Proceedings of the 32nd Annual ACM Symposium on Theory of Computing (Association of Computing Machinery, New York, 2000), pp. 163–170.

⋆⋆ Kleinberg, J. Navigation in a small world. Nature, 406, 845 (2000).
Kleinberg later used a similar approach to study the spread of information in networks via what computer scientists call a gossip protocol:

• Kleinberg, J. Small-world phenomena and the dynamics of information. In Dietterich, T. G., Becker, S., and Ghahramani, Z. (eds.), Advances in Neural Information Processing Systems (NIPS), 14 (MIT Press, Cambridge, MA, 2002).

(٤) رد علم الاجتماع

The paper that resulted from my collaboration with Mark Newman and Peter Dodds, incorporating notions of social identity and social distance into the small-world search problem, is:

⋆⋆ Watts, D. J., Dodds, P. S., and Newman, M. E. J. Identity and search in social networks. Science, 296, 1302–1305 (2002).
The findings of the so-called reverse small-world experiment that corroborated some of our theoretical predictions were published in:

⋆⋆ Killworth, P. D., and Bernard, H. R. The reverse small world experiment. Social Networks, 1, 159–192 (1978).

⋆ Bernard, H. R., Killworth, P. D., Evans, M. J., McCarty, C., and Shelly, G. A. Studying relations cross-culturally. Ethnology, 27(2), 155–179 (1988).

(٥) البحث في شبكات الند للند

A discussion of the problems facing peer-to-peer networks like Gnutella is:

⋆⋆ Ritter, J. P. Why Gnutella can’t scale. No really (working paper, available on-line at http://www.darkridge.com/~jpr5/doc/gnutella.html, 2000).
Two search algorithms that take advantage of Gnutella’s apparent scale-free character are presented in:

• Adamic, L. A., Lukose, R. M., Puniyani, A. R., and Huberman, B. A. Search in power-law networks. Physical Review E, 64, 046135 (2001).

• Kim, B. J., Yoon, C. N., Han, S. K., and Jeong, H. Path finding strategies in scale-free networks. Physical Review E, 65, 027103 (2002).
And a discussion of the problems associated with creating easily searchable distributed databases in the context of a multinational consulting firm is:

⋆ Mannville, B. Complex adaptive knowledge management: A case study from McKinsey and Company. In Clippinger, J. H. (ed.), The Biology of Business: Decoding the Natural Laws of the Enterprise (Jossey-Bass, San Francisco, 1999), chapter 5.
Some other approaches that have been proposed specifically for the purpose of finding information on the World Wide Web are dealt with in the following:

⋆⋆ Brin, S., and Page, L. The anatomy of a large-scale hypertextual web search engine. Computer Networks, 30, 107–117 (1998).

• Gibson, D., Kleinberg, J., and Raghavan, P. Inferring Web communities from link topology. In Proceedings of the 9th ACM Conference on Hypertext and Hypermedia (Association for Computing Machinery, Networks 1998), pp. 225–234.

• Kleinberg, J. Authoritative sources in a hyperlinked environment. Journal of the ACM, 46, 604–632 (1999).

⋆⋆ Lawrence, S., and Giles, C. L. Accessibility of information on the web. Nature, 400, 107–109 (1999).

الفصل السادس: الأوبئة والأعطال

(١) المنطقة الحارة

Richard Preston’s gripping account of the Ebola outbreak in Reston, Virginia, along with a brief history of Ebola, can be found in his book:

⋆ Preston, R. The Hot Zone (Random House, New York, 1994).
Additional Ebola facts were derived from:

⋆ Harden, B. Dr. Matthew’s passion. New York Times Magazine, February 18, 2001, pp. 24–62.

(٢) فيروسات الإنترنت

The account of the e-mail sent by Claire Swire was taken from a New York Times article:

⋆ Lyall, S. Return to sender, please. New York Times, December 24, 2000, Week in Review, p. 2.
A chronology of the Melissa virus can be found at http://www.cert.org/ advisories/CA-1999-04.html.
Records of all registered computer viruses and their histories, including time of first detection, known number of computers infected, and first release of antiviral software, can be found at the Virus Bulletin: http://www.virusbtn.com/. Virus alerts, along with other Internet-related security information, are published and maintained by CERT, based in the Software Engineering Institute at Carnegie Mellon University in Pittsburgh. Their Web site is http://www.cert.org/.
A discussion of the relationship between epidemiology and computer viruses in the age of the Internet is contained in the following:

• Kephart, J. O., White, S. R., and Chess, D. M. Computer viruses and epidemiology. IEEE Spectrum, 30(5), 20–26 (1993).

⋆⋆ Kephart, J. O., Sorkin, G. B., Chess, D. M., and White, S. R. Fighting computer viruses. Scientific American, 277(5), 56–61 (1997).

(٣) رياضيات الأوبئة

The classic papers of Kermack and McKendrick, on which most of modern mathematical epidemiology is based, are:

•• Kermack, W. O., and McKendrick, A. G. A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London, Series A, 115, 700–721 (1927).

•• Kermack, W. O., and McKendrick, A. G. Contributions to the mathematical theory of epidemics. II. The problem of endemicity. Proceedings of the Royal Society of London, Series A, 138, 55–83 (1932).

•• Kermack, W. O., and McKendrick, A. G. Contributions to the mathematical theory of epidemics. III. Further studies of the problem of endemicity. Proceedings of the Royal Society of London, Series A, 141, 94–122 (1933).
The standard text of mathematical epidemiology, and one that treats the SIR model in considerable detail, is:

• Bailey, N. T. J. The Mathematical Theory of Infectious Diseases and Its Applications (Hafner Press, New York, 1975).
Other good references are:

• Bartholomew, D. J. Stochastic Models for Social Processes (Wiley, New York, 1967).

• Anderson, R. M., and May, R. M. Infectious Diseases of Humans (Oxford University Press, Oxford, 1991).

• Murray, J. D. Mathematical Biology, 2d ed. (Springer, Heidelberg, 1993).
A small but excellent collection of papers dealing with the spread of infectious diseases on networks is:

•• Ball, F., Mollison, D., and Scalia-Tomba, G. Epidemics with two levels of mixing. Annals of Applied Probability, 7(1), 46–89 (1997).

⋆⋆ Hess, G. Disease in metapopulation models: Implications for conservation. Ecology, 77, 1617–1632 (1996).

⋆⋆ Kareiva, P. Population dynamics in spatially complex environments: Theory and data. Philosophical Transactions of the Royal Society of London, Series B, 330, 175–190 (1988).

• Kretschmar, M., and Morris, M. Measures of concurrency in networks and the spread of infectious disease. Mathematical Biosciences, 133, 165–195 (1996).

⋆⋆ Longini, I. M., Jr. A mathematical model for predicting the geographic spread of new infectious agents. Mathematical Biosciences, 90, 367–383 (1988).

• Sattenspiel, L., and Simon, C. P. The spread and persistence of infectious diseases in structured populations. Mathematical Biosciences, 90, 341–366 (1988).

(٤) الأوبئة في عالم صغير

The most complete account of the early work on disease spreading on small-world networks is chapter 6 of:

⋆⋆ Watts, D. J. Small Worlds: The Dynamics of Networks between Order and Randomness (Princeton University Press, Princeton, NJ, 1999).
A number of subsequent results about epidemics on networks have been published in the following papers:

• Boots, M., and A. Sasaki. “Small worlds” and the evolution of virulence: Infection occurs locally and at a distance. Proceedings of the Royal Society of London, Series B, 266, 1933–1938 (1999).

• Keeling, M. J. The effects of local spatial structure on epidemiological invasions. Proceedings of the Royal Society of London, Series B, 266, 859–867 (1999).

• Kuperman, M., and Abramson, G. Small world effect in an epidemiological model. Physical Review Letters, 86, 2909–2912 (2001).
Some excellent works on the foot-and-mouth epidemic, and a fine example of mathematical modeling contributing to policy decisions, are:

⋆⋆ Ferguson, N. M., Donnelly, C. A., and Anderson, R. M. The foot-and-mouth epidemic in Great Britain: Pattern of spread and impact of interventions. Science, 292, 1155–1160 (2001).

⋆⋆ Ferguson, N. M., Donnelly, C. A., and Anderson, R. M. Transmission intensity and impact of control policies on the foot and mouth epidemic in Great Britain. Nature, 413, 542–548 (2001).

⋆⋆ Keeling, M. J., Woolhouse, M. E. J., Shaw, D. J., Matthews, L., Chase-Topping, M., Haydon, D. T., Cornell, S. J., Kappey, J., Wilesmith, J., and Grenfell, B. T. Dynamics of the 2001 UK foot and mouth epidemic: Stochastic dispersal in a heterogeneous landscape. Science, 294, 813–817 (2001).
The discovery that diseases spreading in scale-free networks don’t exhibit an epidemic threshold is reported in:

• Pastor-Satorras, R., and Vespignani, A. Epidemic spreading in scale-free networks. Physical Review Letters, 86, 3200–3203 (2001).
Pastor-Satorras and Vespignani have continued to work on disease spreading in scale-free networks. Their findings are summarized in:

• Pastor-Satorras, R., and Vespignani, A. Epidemics and immunization in scale-free networks. In Bornholdt, S., and Schuster, H. G. (eds.), Handbook of Graphs and Networks: From the Genome to the Internet (Wiley-VCH, Berlin, 2002).
Some empirical support for their assumption of a scale-free e-mail network is reported in:

• Ebel, H., Mielsch, L. I., and Bornholdt, S. Scale-free topology of e-mail networks. Physical Review E, 66, 035103 (2002).
The public health impact of needle exchange programs is analyzed in a report for the Journal of the American Medical Association by the Center for AIDS Prevention Studies, University of California, San Francisco, found at http://www.ama-assn.org/special/hiv/preventn/prevent3.htm.

An earlier report prepared for the Centers for Disease Control and Prevention can be found at http://www.caps.ucsf.edu/capsweb/publications/ needlereport.html.

(٥) نماذج التخلل للأمراض

The best introduction to the subject of percolation is the following (which even manages to be funny in places):

• Stauffer, D., and Aharony, A. Introduction to Percolation Theory (Taylor and Francis, London, 1992).
The details of my work with Mark Newman on a site percolation approach to disease spreading on small-world network are given in:

• Newman, M. E. J., and Watts, D. J. Scaling and percolation in the small-world network model. Physical Review E, 60, 7332–7342 (1999).

(٦) الشبكات والفيروسات ومايكروسوفت

Mark Newman and Cris Moore’s work on site and bond percolation is described in the following:

• Moore, C., and Newman, M. E. J. Epidemics and percolation in small-world networks. Physical Review E, 61, 5678–5682 (2000).

•• Moore, C., and Newman, M. E. J. Exact solution of site and bond percolation on small-world networks. Physical Review E, 62, 7059–7064 (2000).

(٧) الأعطال والقوة

The original paper using percolation ideas to quantify network robustness is:

⋆⋆ Albert, R., Jeong, H., and Barabási, A. L. Attack and error tolerance of complex networks. Nature, 406, 378–382 (2000).
Soon after, a series of papers examined the topic in greater detail. They are:

• Callaway, D. S., Newman, M. E. J., Strogatz, S. H., and Watts, D. J. Network robustness and fragility: Percolation on random graphs. Physical Review Letters, 85, 5468–5471 (2000).

• Cohen, R., Erez, K., ben-Avraham, D., and Havlin, S. Resilience of the Internet to random breakdowns. Physical Review Letters, 85, 4626–4628 (2000).

• Cohen, R., Erez, K., ben-Avraham, D., and Havlin, S. Breakdown of the Internet under intentional attack. Physical Review Letters, 86, 3682–3685 (2001).

الفصل السابع: القرارات والأوهام وجنون الجماهير

(١) اقتصاديات التيوليب

Charles Mackay’s classic account of mania, financial and otherwise, has been reprinted many times. A relatively recent version is:

⋆ Mackay, C. Extraordinary Popular Delusions and the Madness of Crowds (Harmony Books, New York, 1980).
Some other recent treatises on the same subject are:

⋆ Kindleberger, C. P. Manias, Panics, and Crashes: A History of Financial Crises, 4th ed. (Wiley, New York, 2000).

⋆ Shiller, R. J. Irrational Exuberance (Princeton University Press, Princeton, NJ, 2000).

(٢) الخوف والطمع والعقلانية

Adam Smith’s discussion of rationally optimizing agents, including his reference to the invisible hand, is in:

⋆ Smith, A. The Wealth of Nations, Vol. 1, Book 4 (University of Chicago Press, Chicago, 1976), chapter 2, p. 477.
The paradox of the efficient market hypothesis is described in:

⋆ Chancellor, E. Devil Take the Hindmost: A History of Financial Speculation (Farrar, Straus and Giroux, New York, 1999).
And some recent work on constructing a more realistic vision of both investor and financial-market behavior, in which dynamics is a crucial ingredient, is:

• Farmer, J. D. Market force, ecology, and evolution. Industrial and Corporate Change, forthcoming (2002).

• Farmer, J. D., and Joshi, S. The price dynamics of common trading strategies. Journal of Economic Behavior and Organization, 49(2), 149–171 (2002).

⋆⋆ Farmer, J. D., and Lo, A. Frontiers of finance: Evolution and efficient markets. Proceedings of the National Academy of Sciences, 96, 9991-9992 (1999).

(٣) القرارات الجمعية

The technical paper by Natalie Glance and Bernardo Huberman, describing the diner’s dilemma and the conditions under which it can be resolved, is:

• Glance, N. S., and Huberman, B. A. The outbreak of cooperation. Journal of Mathematical Sociology, 17(4), 281–302 (1993).
A more accessible description of the same results is:

⋆ Glance, N. S., and Huberman, B. A. The dynamics of social dilemmas. Scientific American, 270(3), 76–81 (1994).
The literature on the evolution of cooperation is gigantic and spans several disciplines—evolutionary biology, economics, political science, and sociology in particular. It is impossible even to provide a representative list of publications, but some important contributions are:

⋆⋆ Axelrod, R. The Evolution of Cooperation (Basic Books, New York, 1984).

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

• Boorman, S. A., and Levitt, P. R. The Genetics of Altruism (Academic Press, New York, 1980).

⋆⋆ Boyd, R. S., and Richerson, P. J. The evolution of reciprocity in sizable groups. Journal of Theoretical Biology, 132, 337–356 (1988).

⋆⋆ Hardin, G. The tragedy of the commons. Science, 162, 1243–1248 (1968).

⋆⋆ Huberman, B. A., and Lukose, R. M. Social dilemmas and Internet congestion. Science, 277, 535–537 (1997).

⋆⋆ Nowak, M. A., and May, R. M. Evolutionary games and spatial chaos. Nature, 359, 826–829 (1992).

⋆⋆ Olson, M. The Logic of Collective Action: Public Goods and the Theory of Groups (Harvard University Press, Cambridge, MA, 1965).

⋆ Ostrom, E., Burger, J., Field, C. B., Norgaard, R. B., and Policansky, D. Revisiting the commons: Local lessons, global challenges. Science, 284, 278–282 (1999).

(٤) سلاسل المعلومات

The literature on information cascades is, again, multidisciplinary and eclectic. Some examples are:

⋆⋆ Aguirre, B. E., Quarantelli, E. L., and Mendoza, J. L. The collective behavior of fads: The characteristics, effects, and career of streaking. American Sociological Review, 53, 569–584 (1988).

• Banerjee, A. V. A simple model of herd behavior. Quarterly Journal of Economics, 107, 797–817 (1992).

• Bikhchandani, S., Hirshleifer, D., and Welch, I. A theory of fads, fashion, custom and cultural change as informational cascades. Journal of Political Economy, 100(5), 992–1026 (1992).

⋆⋆ Lohmann, S. The dynamics of informational cascades: The Monday demonstrations in Leipzig, East Germany, 1989–91. World Politics, 47, 42–101 (1994).

(٥) مؤثرات المعلومات الخارجية

A description of Asch’s original experiment is given in:

⋆ Asch, S. E. Effects of group pressure upon the modification and distortion of judgments. In Cartwright, D., and Zander, A. (eds.), Group Dynamics: Research and Theory (Row, Peterson, Evanston, IL, 1953), pp. 151–162.
Herbert Simon’s theory of bounded rationality is espoused in:

⋆⋆ Simon, H. A., Egidi, M., and Marris, R. L. Economics, Bounded Rationality and the Cognitive Revolution (Edward Elgar, Brookfield, VT, 1992).

(٦) المؤثرات الخارجية القسرية

The spread of crime via a network of peer pressure relationships is considered (in a theoretical manner) in:

⋆⋆ Glaeser, E. L., Sacerdote, B., and Schheinkman, J. A. Crime and social interactions. Quarterly Journal of Economics, 111, 507–548 (1996).
The paper introducing the concept of a spiral of silence in voting behavior is:

⋆ Noelle-Neumann, E. Turbulences in the climate of opinion: Methodological applications of the spiral of silence theory. Public Opinion Quarterly, 41(2), 143–158 (1977).

(٧) مؤثرات السوق الخارجية

The principal exponent of what is now called lock-in via increasing returns is the economist Brian Arthur. His groundbreaking paper (which took him many years to find a journal that would publish it) is:

• Arthur, W. B. Competing technologies, increasing returns, and lock-in by historical events. Economic Journal, 99(394), 116–131 (1989).
Another, slightly different, approach to the topic of increasing returns is espoused in:

• Romer, P. Increasing returns and long-run growth. Journal of Political Economy, 94(5), 1002–1034 (1986).
Although the authors do not link it to the subject of network externalities, the importance of complementarities is emphasized in:

• Milgrom, P., and Roberts, J. The economics of modern manufacturing: Technology, strategy, and organization. American Economic Review, 80(3), 511–528 (1990).
Meanwhile, the prevailing economics approach to so-called network externalities is described in:

⋆⋆ Economides, N. The economics of networks. International Journal of Industrial Organization, 16(4), 673–699 (1996).

(٨) مؤثرات التنسيق الخارجية

Although neither of these papers uses the term, the relevance of externalities to decisions about cooperation is evident in:

• Glance, N. S., and Huberman, B. A. The outbreak of cooperation. Journal of Mathematical Sociology, 17(4), 281–302 (1993).

⋆⋆ Kim, H., and Bearman, P. The structure and dynamics of movement participation. American Sociological Review, 62(1), 70–94 (1997).

(٩) صناعة القرار اجتماعيًّا

The report on body piercing is:

⋆ Harden, B. Coming to grips with the enduring appeal of body piercing. New York Times, February 12, 2002, p. A16.

الفصل الثامن: الحدود والسلاسل وقابلية التنبؤ

(١) نماذج حدود القرارات

The earliest use of threshold models as a way of understanding collective decision making is probably:

⋆⋆ Schelling, T. C. A study of binary choices with externalities. Journal of Conflict Resolution, 17(3), 381–428 (1973).
Another early classic is:

⋆⋆ Granovetter, M. Threshold models of collective behavior. American Journal of Sociology, 83(6), 1420–1443 (1978).
The actual derivation of a threshold model depends on what kind of decision an individual is making, and what sort of decision externalities pertain. Some examples of quite different derivations, all of which effectively generate threshold rules are:

• Arthur, W. B., and Lane, D. A. Information contagion. Structural Change and Economic Dynamics, 4(1), 81–103 (1993).

• Boorman, S. A., and Levitt, P. R. The Genetics of Altruism (Academic Press, New York, 1980).

• Durlauf, S. N. A framework for the study of individual behavior and social interactions. Sociological Methodology, 31, 47–87 (2001).

• Glance, N. S., and Huberman, B. A. The outbreak of cooperation. Journal of Mathematical Sociology, 17(4), 281–302 (1993).

• Morris, S. N. Contagion. Review of Economic Studies, 67, 57–78 (2000).

(٣) السلاسل في الشبكات الاجتماعية

Some information about Ithaca hours can be found in:

⋆ Glover, P. Grassroots economics. In Context, 41, 30 (1995).

⋆ Morse, M. Dollars or sense. Utne Reader, 99 (September–October 1999).
Everett Rogers’ classic reference on the diffusion of innovations, in which much of the still-current terminology was introduced, was first published in 1962. It is now in its fourth edition:

⋆ Rogers, E. The Diffusion of Innovations, 4th ed. (Free Press, New York, 1995).
A valiant attempt to combine Rogers’ ideas with concepts from social network analysis is by one of Rogers’ students, Thomas Valente:

⋆⋆ Valente, T. W. Network Models of the Diffusion of Innovations (Hampton Press, Cresskill, NJ, 1995).

⋆ Coleman, J. S., Katz, E., and Menzel, H. The diffusion of an innovation among physicians. Sociometry, 20(4), 253–270 (1957).

(٤) السلاسل والتخلل

The paper summarizing the threshold model approach to information cascades on networks is:

• Watts, D. J. A simple model of global cascades on random networks. Proceedings of the National Academy of Sciences, 99, 5766–5771 (2002).

(٥) التحولات الطورية والسلاسل

Malcolm Gladwell’s engaging discussion of social contagion is:

⋆ Gladwell, M. The Tipping Point: How Little Things Can Make a Big Difference (Little, Brown, New York, 2000).

(٦) تجاوز الصدع

Geoffrey Moore’s descriptive account of the “chasm” between early adopters and the early to late majority is given in:

⋆ Moore, G. A. Crossing the Chasm: Marketing and Selling High-Tech Products to Mainstream Customers (Harper Business, New York, 1999).

(٧) وجهة نظر غير خطية للتاريخ

The distinction between quality and success is made apparent in Art De Vany’s study of the movie industry:

⋆⋆ De Vany, A., and Lee, C. Quality signals in information cascades and the dynamics of motion picture box office revenues: A computational model. Journal of Economic Dynamics and Control, 25, 593–614 (2001).

• De Vany, A. S., and Walls, W. D. Bose-Einstein dynamics and adaptive contracting in the motion picture industry. Economic Journal, 106, 1493–1514 (1996).

(٩) عودة إلى القوة

The related notions of normal accidents and robust-yet-fragile systems are presented in two very different works:

⋆ Perrow, C. Normal Accidents: Living with High-Risk Technologies (Basic Books, New York, 1984).

• Carlson, J. M., and Doyle, J. Highly optimized tolerance: A mechanism for power laws in designed systems. Physical Review E, 60(2), 1412–1427 (1999).

الفصل التاسع: الابتكار والتكيُّف والتعافي

(١) أزمة تويوتا-آيسين

The account of the Toyota-Aisin crisis on which my description is based is:

⋆ Nishiguchi, T., and Beaudet, A. Fractal design: Self-organizing links in supply chain management. In Von Krogh, G., Nonaka, I., and Nishiguchi, T. (eds.), Knowledge Creation: A Source of Value (Macmillan, London, 2000).
Another paper about the remarkable Toyota group that guided our thinking on innovation is:

⋆ Ward, A., Liker, J. K., Cristiano, J. J., and Sobek, D. K. The second Toyota paradox: How delaying decisions can make better cars faster. Sloan Management Review, 36(3), 43–51 (1995).

(٢) الأسواق والهياكل الهرمية

The original text—and still one of the greatest—on industrial organization is:

⋆ Smith, A. The Wealth of Nations (University of Chicago Press, Chicago, 1976).
A precursor to Coase’s theory of transaction costs was Frank Knight’s claim that firms exist to reduce uncertainty:

⋆⋆ Knight, F. H. Risk, Uncertainty, and Profit (London School of Economics and Political Science, London, 1933).
And Ronald Coase’s original argument of transaction costs as the basis for the firm is explicated in:

⋆ Coase, R. The nature of the firm. Economica, n.s., 4 (November 1937).
Several decades later, Coase is still trying to get his ideas accepted by mainstream economics. His latest attempt is:

⋆ Coase, R. The Nature of the Firm (Oxford University Press, Oxford, 1991).
The chief proponent of the hierarchical structure of firms is Oliver Williamson, whose views are expressed comprehensively in:

⋆⋆ Williamson, O. E. Markets and Hierarchies (Free Press, New York, 1975).
A shorter version is:

⋆⋆ Williamson, O. E. Transaction cost economics and organization theory. In Smelser, N. J., and Swedberg, R. (eds.), The Handbook of Economic Sociology (Princeton University Press, Princeton, NJ, 1994), pp. 77–107.
The superiority of the hierarchy has been extensively formalized and developed in recent years by a small group of economists, led by Roy Radner. Some of the principal works of this literature are:

• Bolton, P., and Dewatripont, M. The firm as a communication network. Quarterly Journal of Economics, 109(4), 809–839 (1994).

• Radner, R. The organization of decentralized information processing. Econometrica, 61(5), 1109–1146 (1993).

• Radner, R. Bounded rationality, indeterminacy, and the theory of the firm. Economic Journal, 106, 1360–1373 (1996).

• Van Zandt, T. Decentralized information processing in the theory of organizations. In Sertel, M. (ed.), Contemporary Economic Issues, vol. 4: Economic Design and Behavior p. 125–160 (Macmillan, London, 1999), chapter 7.

(٣) التقسيمات الصناعية

Michael Piore and Chuck Sabel’s groundbreaking book on the changing nature of the global economy is:

⋆ Piore, M. J., and Sabel, C. F. The Second Industrial Divide: Possibilities for Prosperity (Basic Books, New York, 1984).

(٤) الغموض

The paper describing Honda’s system for identifying problems in their manufacturing plants is:

⋆ MacDuffie, J. P. The road to “root cause”: Shop-floor problemsolving at three auto assembly plants. Management Science, 43, 4 (1997).
A variety of approaches to the theory of the internal architecture of the firm have been taken within the economics, sociology, and business communities. It is a vast literature. An eclectic collection of readings, with no claim to being exhaustive or even representative, is as follows:

⋆ Chandler, A. D. The Visible Hand: The Managerial Revolution in American Business (Belknap Press of Harvard University Press, Cambridge, MA, 1977).

⋆ Clippinger, J. (ed.). The Biology of Business: Decoding the Natural Laws of the Enterprise (Jossey-Bass, San Francisco, 1999).

• Fama, E. F. Agency problems and the theory of the firm. Journal of Political Economy, 88, 288–307 (1980).

⋆⋆ Hart, O. Firms, Contracts and Financial Structure (Oxford University Press, New York, 1995).

⋆⋆ March, J. G., and Simon, H. A. Organizations (Blackwell, Oxford, 1993).

⋆⋆ Nelson, R. R., and Winter, S. G. An Evolutionary Theory of Economic Change (Belknap Press of Harvard University Press, Cambridge, MA, 1982).

⋆⋆ Powell, W., and DiMaggio, P. (eds.). The New Institutionalism in Organizational Analysis (Chicago, University of Chicago Press, 1991).

• Sah, R. K., and Stiglitz, J. E. The architecture of economic systems: Hierarchies and polyarchies. American Economic Review, 76(4), 716–727 (1986).

(٥) الطريقة الثالثة

An indication of Chuck’s understanding of the problem at the time we started working together is given in the following:

⋆ Helper, S., MacDuffie, J. P., and Sabel, C. F. Pragmatic collaborations: Advancing knowledge while controlling opportunism. Industrial and Corporate Change, 9(3), 443–488 (2000).

⋆ Sabel, C. F. Diversity, not specialization: The ties that bind the (new) industrial district. In Quadrio Curzio, A., and Fortis, M. (eds.), Complexity and Industrial Clusters: Dynamics and Models in Theory and Practice (Physica-Verlag, Heidelberg, 2002).

(٦) التكيف مع الغموض

Perhaps the clearest exposition of the conundrum faced by firms in ambiguous environments, and their need to be both adapted and adaptable, is that by David Stark in his work on heterarchies:

⋆ Stark, D. C. Recombinant property in East European capitalism. American Journal of Sociology, 101(4), 993–1027 (1996).

⋆ Stark, D. C. Heterarchy: Distributing authority and organizing diversity. In Clippinger, J. H. (ed.), The Biology of Business: Decoding the Natural Laws of the Enterprise (Jossey-Bass, San Francisco, 1999), chapter 7.

⋆ Stark, D. C., and Bruszt, L. Postsocialist Pathways: Transforming Politics and Property in East Central Europe (Cambridge University Press, Cambridge, 1998).

(٧) الشبكات متعددة المستويات

The properties of team-based, multiscale, and core-periphery networks are outlined in:

• Dodds, P. S., Watts, D. J., and Sabel, C. F. The structure of optimal redistribution networks. Institute for Social and Economic Research and Policy Working Paper, Columbia University (2002).

الفصل العاشر: نهاية البداية

The use of New York City (or more precisely, the borough of Manhattan) as an example of a complex system was inspired by John Holland’s opening chapter in:

⋆ Holland, J. H. Hidden Order: How Adaptation Builds Complexity (Perseus, Cambridge, MA, 1996).

(١) الحادي عشر من سبتمبر

An excellent and detailed account of the September 11 attacks on the World Trade Center, and the monumental recovery effort that followed its collapse, is given in:

⋆ Langewiesche, W. American Ground: Unbuilding the World Trade Center (North Point Press, New York, 2002).
The information about the police department’s communications predicament was derived from:

⋆ Rashbaum, W. K. Police officers swiftly show inventiveness during crisis. New York Times, September 17, 2001, p. A7.
The story about Cantor Fitzgerald was related by one of the survivors—the director of marketing and communications—who spoke at a roundtable discussion of business leaders at Columbia University on December 5, 2001. The roundtable was organized by David Stark and John Kelly, directors of Columbia’s Center for Organizational Innovation and Interactive Design Lab, respectively, and sponsored by Dr. Susan Gitelson.

The article by Paul Krugman considering the economic consequences of the September 11 attacks in the context of an already faltering economy is:

⋆ Krugman, P. Fear itself. New York Times Magazine, September 30, 2001, p. 36.

(٢) دروس لعصر متشابك

An engaging and insightful account of the 1997 Asian crisis is contained in:

⋆ Friedman, T. L. The Lexus and the Olive Tree: Understanding Globalization (Farrar, Straus and Giroux, New York, 1999).
Quite a lot of Harry Potter–related information can be found at http://www.insideharrypotter.com.
And finally, a brief but illuminating account of the problems that beset Long Term Capital Management in the fall of 1998, is:

⋆ MacKenzie, D. Fear in the markets. London Review of Books, 22(8), 31–32 (2000).

الفصل الحادي عشر: العالم يتضاءل: عام آخر في العصر المتشابك

⋆⋆ Dodds, P. S., Muhamad, R., and Watts, D. J. An experimental study of search in global social networks. Science, 301, 827–829 (2003).

• Dodds, P. S., Watts, D. J., and Sabel, C. F. Information exchange and the robustness of organizational networks. Proceedings of the National Academy of Sciences, 100, 12516–12521 (2003).

•• Kempe, D., Kleinberg, J., and Tardos, E. Maximizing the spread of influence through a social network. Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2003).

•• Newman, M. E. J. The structure and function of complex networks. SIAM Review, 45, 167–256 (2003).