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 & Context (language use). The organization has 558 authors who have published 4558 publications receiving 396015 citations. The organization is also known as: SFI.

Preferential attachment growth model and nonextensive statistical mechanics

Abstract: We introduce a two-dimensional growth model where every new site is located, at a distance r from the barycenter of the pre-existing graph, according to the probability law 1/r2 + αG (αG > 0), and is attached to (only) one pre-existing site with a probability ki/riαA (αA ≥ 0; ki is the number of links of the i-th site of the pre-existing graph, and ri its distance to the new site). Then we numerically determine that the probability distribution for a site to have k links is asymptotically given, for all values of αG, by P(k) eq−k/κ, where eqx ≡ [1 + (1 − q)x]1/(1 − q) is the function naturally emerging within nonextensive statistical mechanics. The entropic index is numerically given (at least for αA not too large) by q = 1 + (1/3)e−0.526 αA, and the characteristic number of links by κ 0.1 + 0.08 αA. The αA = 0 particular case belongs to the same universality class to which the Barabasi-Albert model belongs. In addition to this, we have numerically studied the rate at which the average number of links ki increases with the scaled time t/i; asymptotically, ki (t/i)β, the exponent being close to β = ½(1 − αA) for 0 ≤ αA ≤ 1, and zero otherwise. The present results reinforce the conjecture that the microscopic dynamics of nonextensive systems typically build (for instance, in Gibbs Γ-space for Hamiltonian systems) a scale-free network.

The regulatory network of E. coli metabolism as a boolean dynamical system exhibits both homeostasis and flexibility of response

Abstract: Elucidating the architecture and dynamics of large scale genetic regulatory networks of cells is an important goal in systems biology. We study the system level dynamical properties of the genetic network of Escherichia coli that regulates its metabolism, and show how its design leads to biologically useful cellular properties. Our study uses the database (Covert et al., Nature 2004) containing 583 genes and 96 external metabolites which describes not only the network connections but also the boolean rule at each gene node that controls the switching on or off of the gene as a function of its inputs. We have studied how the attractors of the boolean dynamical system constructed from this database depend on the initial condition of the genes and on various environmental conditions corresponding to buffered minimal media. We find that the system exhibits homeostasis in that its attractors, that turn out to be fixed points or low period cycles, are highly insensitive to initial conditions or perturbations of gene configurations for any given fixed environment. At the same time the attractors show a wide variation when external media are varied implying that the system mounts a highly flexible response to changed environmental conditions. The regulatory dynamics acts to enhance the cellular growth rate under changed media. Our study shows that the reconstructed genetic network regulating metabolism in {\it E. coli} is hierarchical, modular, and largely acyclic, with environmental variables controlling the root of the hierarchy. This architecture makes the cell highly robust to perturbations of gene configurations as well as highly responsive to environmental changes. The twin properties of homeostasis and response flexibility are achieved by this dynamical system even though it is not close to the edge of chaos.

Using Gossips to Spread Information: Theory and Evidence from Two Randomized Controlled Trials

Abstract: Can we identify highly central individuals in a network without collecting network data, simply by asking community members? Can seeding information via such nominated individuals lead to significantly wider diffusion than via randomly chosen people, or even respected ones? In two separate large field experiments in India, we answer both questions in the affirmative. In particular, in 521 villages in Haryana, we provided information on monthly immunization camps to either randomly selected individuals (in some villages) or to individuals nominated by villagers as people who would be good at transmitting information (in other villages). We find that the number of children vaccinated every month is 22% higher in villages in which nominees received the information. We show that people’s knowledge of who are highly central individuals and good seeds can be explained by a model in which community members simply track how often they hear gossip about others. Indeed, we find in a third data set that nominated seeds are central in a network sense, and are not just those with many friends or in powerful positions.

Electronic Structure Calculations and the Ising Hamiltonian

Abstract: Obtaining exact solutions to the Schrodinger equation for atoms, molecules, and extended systems continues to be a “Holy Grail” problem which the fields of theoretical chemistry and physics have been striving to solve since inception. Recent breakthroughs have been made in the development of hardware-efficient quantum optimizers and coherent Ising machines capable of simulating hundreds of interacting spins with an Ising-type Hamiltonian. One of the most vital questions pertaining to these new devices is, “Can these machines be used to perform electronic structure calculations?” Within this work, we review the general procedure used by these devices and prove that there is an exact mapping between the electronic structure Hamiltonian and the Ising Hamiltonian. Additionally, we provide simulation results of the transformed Ising Hamiltonian for H2 , He2 , HeH+, and LiH molecules, which match the exact numerical calculations. This demonstrates that one can map the molecular Hamiltonian to an Ising-type Hami...