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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
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>
>       On Dec 4, 2017, at 12:56 PM, martina morris <[log in to unmask]> wrote:
>
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>
>       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:
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>
>                  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:
>
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>
>                  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
>
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>
>                  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. Valente, PhD
>
>                  Professor and Interim Chair
>
>                  Department of Preventive Medicine
>
>                  Keck School of Medicine
>
>                  University of Southern California
>
>                  Soto Street Building, Suite 330
>
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