Santa Fe Institute

About: Santa Fe Institute is a nonprofit organization based out in Santa Fe, New Mexico, United States. It is known for research contribution in the topics: Population & Complex network. The organization has 558 authors who have published 4558 publications receiving 396015 citations. The organization is also known as: SFI.

Understanding mobility in a social petri dish

Abstract: Despite the recent availability of large data sets on human movements, a full understanding of the rules governing motion within social systems is still missing, due to incomplete information on the socio-economic factors and to often limited spatio-temporal resolutions. Here we study an entire society of individuals, the players of an online-game, with complete information on their movements in a network-shaped universe and on their social and economic interactions. Such a "socio-economic laboratory" allows to unveil the intricate interplay of spatial constraints, social and economic factors, and patterns of mobility. We find that the motion of individuals is not only constrained by physical distances, but also strongly shaped by the presence of socio-economic areas. These regions can be recovered perfectly by community detection methods solely based on the measured human dynamics. Moreover, we uncover that long-term memory in the time-order of visited locations is the essential ingredient for modeling the trajectories.

Nonadditive entropy: The concept and its use

Abstract: The thermodynamical concept of entropy was introduced by Clausius in 1865 in order to construct the exact differential dS = \( \delta\)Q/T , where \( \delta\)Q is the heat transfer and the absolute temperature T its integrating factor. A few years later, in the period 1872-1877, it was shown by Boltzmann that this quantity can be expressed in terms of the probabilities associated with the microscopic configurations of the system. We refer to this fundamental connection as the Boltzmann-Gibbs (BG) entropy, namely (in its discrete form) \(\ensuremath S_{BG}=-k\sum_{i=1}^W p_i \ln p_i\) , where k is the Boltzmann constant, and {pi} the probabilities corresponding to the W microscopic configurations (hence ∑Wi=1pi = 1 . This entropic form, further discussed by Gibbs, von Neumann and Shannon, and constituting the basis of the celebrated BG statistical mechanics, is additive. Indeed, if we consider a system composed by any two probabilistically independent subsystems A and B (i.e., \(\ensuremath p_{ij}^{A+B}=p_i^A p_j^B, \forall(i,j)\) , we verify that \(\ensuremath S_{BG}(A+B)=S_{BG}(A)+S_{BG}(B)\) . If a system is constituted by N equal elements which are either independent or quasi-independent (i.e., not too strongly correlated, in some specific nonlocal sense), this additivity guarantees SBG to be extensive in the thermodynamical sense, i.e., that \(\ensuremath S_{BG}(N) \propto N\) in the N ≫ 1 limit. If, on the contrary, the correlations between the N elements are strong enough, then the extensivity of SBG is lost, being therefore incompatible with classical thermodynamics. In such a case, the many and precious relations described in textbooks of thermodynamics become invalid. Along a line which will be shown to overcome this difficulty, and which consistently enables the generalization of BG statistical mechanics, it was proposed in 1988 the entropy \(\ensuremath S_q=k [1-\sum_{i=1}^W p_i^q]/(q-1) (q\in{R}; S_1=S_{BG})\) . In the context of cybernetics and information theory, this and similar forms have in fact been repeatedly introduced before 1988. The entropic form Sq is, for any q\( eq\) 1 , nonadditive. Indeed, for two probabilistically independent subsystems, it satisfies \(\ensuremath S_q(A+B)/k=[S_q(A)/k]+ [S_q(B)/k]+(1-q)[S_q(A)/k][S_q(B)/k] eq S_q(A)/k+S_q(B)/k\) . This form will turn out to be extensive for an important class of nonlocal correlations, if q is set equal to a special value different from unity, noted qent (where ent stands for entropy . In other words, for such systems, we verify that \(\ensuremath S_{q_{ent}}(N) \propto N (N \gg 1)\) , thus legitimating the use of the classical thermodynamical relations. Standard systems, for which SBG is extensive, obviously correspond to qent = 1 . Quite complex systems exist in the sense that, for them, no value of q exists such that Sq is extensive. Such systems are out of the present scope: they might need forms of entropy different from Sq, or perhaps --more plainly-- they are just not susceptible at all for some sort of thermostatistical approach. Consistently with the results associated with Sq, the q -generalizations of the Central Limit Theorem and of its extended Levy-Gnedenko form have been achieved. These recent theorems could of course be the cause of the ubiquity of q -exponentials, q -Gaussians and related mathematical forms in natural, artificial and social systems. All of the above, as well as presently available experimental, observational and computational confirmations --in high-energy physics and elsewhere-- are briefly reviewed. Finally, we address a confusion which is quite common in the literature, namely referring to distinct physical mechanisms versus distinct regimes of a single physical mechanism.

Population modeling of the emergence and development of scientific fields

Abstract: We analyze the temporal evolution of emerging fields within several scientific disciplines in terms of numbers of authors and publications. From bibliographic searches we construct databases of authors, papers, and their dates of publication. We show that the temporal development of each field, while different in detail, is well described by population contagion models, suitably adapted from epidemiology to reflect the dynamics of scientific interaction. Dynamical parameters are estimated and discussed to reflect fundamental characteristics of the field, such as time of apprenticeship and recruitment rate. We also show that fields are characterized by simple scaling laws relating numbers of new publications to new authors, with exponents that reflect increasing or decreasing returns in scientific productivity.