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***** To join INSNA, visit http://www.insna.org ***** If we're venturing outside the field of Networks, then I'd just note that diffusion is a central concept in Epidemiology. There, precedence is generally associated with Kermack/McKendrick 1927 (which led to deterministic models of diffusion) and Reed/Frost 1928 (associated with stochastic models) The Kermack–McKendrick model described the relationship between susceptible, infected and immune individuals in a population (now known as the SIR model, where R refers to recovery with immunity), with the infection curve governed by a "force of infection" and the random mixing of S & I. The Reed–Frost model was a stochastic version, treating the force of infection as a probability of infection given contact between S & I. Both give rise to the standard S-shaped curve in the absence of recovery (the SI model), as susceptibles are depleted. On Tue, 5 Dec 2017, James Holland Jones wrote: > ***** To join INSNA, visit https://urldefense.proofpoint.com/v2/url?u=http-3A__www.insna.org&d=DwIDaQ&c=pZJPUDQ3SB9JplYbifm4nt2lEVG5pWx2KikqINpWlZM&r=uXI5O6HThk1ULkPyaT6h2Ws3RKNKSY__GQ4DuS9UHhs&m=SABUgGPUHxSdwkt9cmkZmOihzwsHWeR1IT7gUXlGMt0&s=uWJb0OPq70sFN0j3mRn09vHiEnlMp08RfRhz25_X09Q&e= ***** Two papers stand out for me in the early history of diffusion. The > first is Einstein's (1905) paper on Brownian motion. In that, Einstein derives what i s often called the "diffusion > approximation," the solution to which is that the density of particles at point x at time t (assuming a starting point of > x=0 and t=0) is normal with mean zero and variance equal to the 2Dt (where D is the diffusion constant). Among other > things, it means that a particle's displacement increases proportional to sqrt(t) rather than linearly with time. The > diffusion approximation is used quite a bit in population biology to estimate stochastic growth rates, > times-to-extinction, etc. The paper I know best on this is Lande and Orzack (1988) but Ludwig (1996) is another important > one. > > The second paper is Fisher's (1937) paper on the spread of an advantageous allele. It's a reaction-diffusion equation > which can yield a traveling-wave solution. In the case of an advantageous allele, the speed of the wave front is given by > its fitness, r. > > Ken Aoki (1987) used the Fisher model for cultural spread and Ammerman and Cavali-Sforza (1971) used it to model the > spread of agriculture in Neolithic Europe. These ideas are largely independent of the diffusion-of-innovations literature > (as exemplified by Rogers) with which we are probably most familiar, but there are clearly addressing related problems. > > Cheers, > Jamie > > -- > James Holland Jones > Associate Professor of Earth System Science & > Senior Fellow, Woods Institute for the Environment > > 473 Via Ortega, Room 140 > Stanford, CA 94305-4216 > > phone: 650-721-2484 > fax: 650-498-5099 > email: [log in to unmask] > url: https://urldefense.proofpoint.com/v2/url?u=https-3A__profiles.stanford.edu_james-2Djones&d=DwIDaQ&c=pZJPUDQ3SB9JplYbifm4nt2lEVG5pWx2KikqINpWlZM&r=uXI5O6HThk1ULkPyaT6h2Ws3RKNKSY__GQ4DuS9UHhs&m=SABUgGPUHxSdwkt9cmkZmOihzwsHWeR1IT7gUXlGMt0&s=i50srbNTdjbB-f9XbsVyaNRbWy-_Wy-hVyymMvbVwx8&e= > > On Dec 4, 2017, at 12:56 PM, martina morris <[log in to unmask]> wrote: > > ***** To join INSNA, visit https://urldefense.proofpoint.com/v2/url?u=http-3A__www.insna.org&d=DwIDaQ&c=pZJPUDQ3SB9JplYbifm4nt2lEVG5pWx2KikqINpWlZM&r=uXI5O6HThk1ULkPyaT6h2Ws3RKNKSY__GQ4DuS9UHhs&m=SABUgGPUHxSdwkt9cmkZmOihzwsHWeR1IT7gUXlGMt0&s=uWJb0OPq70sFN0j3mRn09vHiEnlMp08RfRhz25_X09Q&e= ***** > > Thanks for sharing this info Thomas -- it's very interesting. > > 'Pre-paradigmatic' seems like an apt term insofar as the dominant paradigm today wrt diffusion > processes assumes s-shaped, scalable, exponential curves embedded in models of proportionate > growth. > > > Those of us who work on network structured diffusion have a more general paradigm. Much of this work has > emerged in the context of network modeling of epidemics, so doesn't make it into the Network journals. > > question. A good example is Lynn White's 1966 book Medieval Technology and Social Change, which > traces the development of medieval warfare to innovations in horse saddlery, specifically, the > introduction of the foot stirrup around the 6th CE. However, her description of the > process(es) associated with the 'spreading' and adoption of saddle stirrups is considerably > lumpier than any smooth, s-shaped curve would suggest. > > > And indeed, a network structured by clustering (for whatever reason) would produce just this pattern. > > > On Mon, Dec 4, 2017 at 2:05 PM, Thomas William Valente <[log in to unmask]> wrote: > ***** To join INSNA, visithttps://urldefense.proofpoint.com/v2/url?u=http-3A__www.insna.org&d=DwIDaQ&c=pZJPUDQ3SB9JplYbifm4nt2lEVG5pWx2KikqINpWlZM > &r=uXI5O6HThk1ULkPyaT6h2Ws3RKNKSY__GQ4DuS9UHhs&m=qBebR8TzUx1GyN7zOU3ch4UcXjM8UCRzCIzQQRHSfFw&s=mwnz0lFVeyS-Izj5ihjv6rAqV > BneEk-uaOk6wivszOI&e= ***** > > We classified those studies as pre-paradigmatic, quite a few studies on the diffusion of > arrowheads and other archeologic evidence. The paradigm, however, coalesced with the Ryan & > Gross publication which strongly influenced the Rural Sociology tradition. > > > From: George Barnett [mailto:[log in to unmask]] > Sent: Monday, December 04, 2017 10:03 AM > To: Thomas William Valente > Cc: [log in to unmask] > Subject: Re: [SOCNET] History and origins of diffusion processes > > > Tom & Thomas, > > It actually goes back a whole lot further to the work of Galton (cultural trait > diffusion), and then Pemberton (the diffusion of postage stamps) and Stuart Chapin. I > haven't looked at the early research in 40+ years, but there was lots of research which > preceded Ryan and Gross. > > > George > > George A. Barnett, Ph.D. > > Distinguished Professor Emeritus > > Department of Communication > > 393 Kerr Hall > > University of California – Davis > > Davis, CA 95616-8695 > > [log in to unmask] > > > > On Mon, Dec 4, 2017 at 9:00 AM, Thomas William Valente <[log in to unmask]> wrote: > > ***** To join INSNA, visithttps://urldefense.proofpoint.com/v2/url?u=http-3A__www.insna.org&d=DwIDaQ&c=pZJPUDQ3SB9JplYbifm4nt2lEVG5pWx2KikqINpWlZM > &r=uXI5O6HThk1ULkPyaT6h2Ws3RKNKSY__GQ4DuS9UHhs&m=qBebR8TzUx1GyN7zOU3ch4UcXjM8UCRzCIzQQRHSfFw&s=mwnz0lFVeyS-Izj5ihjv6rAqV > BneEk-uaOk6wivszOI&e= ***** > > Thomas > > Although this isn’t quite what you are looking for, in the 1990-1991 time frame I interview > (along with Everett Rogers) a number of early pioneers of diffusion of innovations research. > We published our findings in this paper: > > > Valente, T. W., & Rogers, E. M. (1995). The origins and development of the diffusion of > innovations paradigm as an example of scientific growth. Science Communication: An > Interdisciplinary Social Science Journal. 16, 238-269. > > > The abstract reads: > > This article traces the emergence of the basic paradigm for early diffusion research created > by two rural sociologists at Iowa State University, Bryce Ryan and Neal C. Gross. The > diffusion paradigm spread to an invisible college of midwestern rural sociological > researchers in the 1950s and 1960s, and then to a larger, interdisciplinary field of > diffusion scholars. By the late 1960s, rural sociologists lost interest in diffusion > studies, > not because it was ineffective scientifically, but because of lack of support for such study > as a consequence of farm overproduction and because most of the interesting research > questions were thought to be answered. > > > -Tom > > > Thomas W. Valente, PhD > > Professor and Interim Chair > > Department of Preventive Medicine > > Keck School of Medicine > > University of Southern California > > Soto Street Building, Suite 330 > > 2001 N Soto Street, MC 9239 > > Los Angeles CA 90089-9239 > > Email: [log in to unmask] > > > ***** To join INSNA, visithttps://urldefense.proofpoint.com/v2/url?u=http-3A__www.insna.org&d=DwIDaQ&c=pZJPUDQ3SB9JplYbifm4nt2lEVG5pWx2KikqINpWlZM > &r=uXI5O6HThk1ULkPyaT6h2Ws3RKNKSY__GQ4DuS9UHhs&m=qBebR8TzUx1GyN7zOU3ch4UcXjM8UCRzCIzQQRHSfFw&s=mwnz0lFVeyS-Izj5ihjv6rAqV > BneEk-uaOk6wivszOI&e= ***** > > If one looks up the word 'diffusion' in the Dictionary of the History of Science, you get > the > standard explanation that 'diffusion' originated in the 19th c with Graham and Maxwell and > has a Latin etymology in the word, diffundere, which means "to spread out." There has to be > more to the story than this, right? > > Earlier references might include the "diffusion of refracted light" in Robert Greene (1727) > and "diffusion of light" in Newton's Optical Lectures (1728). > > > My question for these listservs is, does anyone have any additional insight into the history > and origins of the abstract idea of 'diffusion?' > > > Thank you, > > Thomas Ball > > > > > Thomas W. 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