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.

Generalized Box–MÜller Method for Generating $q$ -Gaussian Random Deviates

Abstract: The q-Gaussian distribution is known to be an attractor of certain correlated systems and is the distribution which, under appropriate constraints, maximizes a generalization of the familiar Shannon entropy. This generalized entropy, or q-entropy, provides the basis of nonextensive statistical mechanics, a theory which is postulated as a natural extension of the standard (Boltzmann-Gibbs) statistical mechanics, and which may explain the ubiquitous appearance of heavy-tailed distributions in both natural and man-made systems. The q-Gaussian distribution is also used as a numerical tool, for example as a visiting distribution in Generalized Simulated Annealing. A simple, easy to implement numerical method for generating random deviates from a q-Gaussian distribution based upon a generalization of the well known Box-Miiller method is developed and presented. This method is suitable for a larger range of q values, -infin < q < 3, than has previously appeared in the literature, and can generate deviates from q-Gaussian distributions of arbitrary width and center. MATLAB code showing a straightforward implementation is also included.

A centralized gene-based HIV-1 vaccine elicits broad cross-clade cellular immune responses in rhesus monkeys

Abstract: One of the major challenges that must be met in developing an HIV-1 vaccine is devising a strategy to generate cellular immunity with sufficient breadth to deal with the extraordinary genetic diversity of the virus. Amino acids in the envelopes of viruses from the same clade can differ by >15%, and those from different clades can differ by >30%. It has been proposed that creating immunogens using centralized HIV-1 gene sequences might provide a practical solution to this problem. Such centralized genes can be generated by employing a number of different strategies: consensus, ancestral, or center of tree sequences. These computer-generated sequences are a shorter genetic distance from any two contemporary virus sequences than those contemporary sequences are from each other. The present study was initiated to evaluate the breadth of cellular immunity generated through immunization of rhesus monkeys with vaccine constructs expressing either an HIV-1 global consensus envelope sequence (CON-S) or a single patient isolate clade B envelope sequence (clade B). We show that vaccine immunogens expressing the single centralized gene CON-S generated cellular immune responses with significantly increased breadth compared with immunogens expressing a wild-type virus gene. In fact, CON-S immunogens elicited cellular immune responses to 3- to 4-fold more discrete epitopes of the envelope proteins from clades A, C, and G than did clade B immunogens. These findings suggest that immunization with centralized genes is a promising vaccine strategy for developing a global vaccine for HIV-1 as well as vaccines for other genetically diverse viruses.

Random graph models for dynamic networks

Abstract: We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of edges are governed by continuous-time Markov processes with rate parameters that can depend on properties of the nodes. In addition to computing equilibrium properties of these models, we demonstrate their use in data analysis and statistical inference, giving efficient algorithms for fitting them to observed network data. This allows us, for instance, to estimate the time constants of network evolution or infer community structure from temporal network data using cues embedded both in the probabilities over time that node pairs are connected by edges and in the characteristic dynamics of edge appearance and disappearance. We illustrate our methods with a selection of applications, both to computer-generated test networks and real-world examples.

Mutation in autocatalytic reaction networks. An analysis based on perturbation theory.

Abstract: A class of kinetic equations describing catalysed and template induced replication, and mutation is introduced. This ODE in its most general form is split into two vector fields, a replication and a mutation field. The mutation field is considered as a perturbation of the replicator equation. The perturbation expansion is a Taylor series in a mutation parameter lambda. First, second and higher order contributions are computed by means of the conventional Rayleigh-Schrodinger approach. Qualitative shift in the positions of rest points and limit cycles on the boundary of the physically meaningful part of concentration space are predicted from flow topologies. The results of the topological analysis are summarized in two theorems which turned out to be useful in applications: the rest point migration theorem (RPM) and the limit cycle migration theorem (LCM). Quantitative expressions for the shifts of rest points are computed directly from the perturbation expansion. The concept is applied to a collection of selected examples from biophysical chemistry and biology.