472 research outputs found
Non-monotonic spontaneous magnetization in a Sznajd-like Consensus Model
Ising or Potts models of ferromagnetism have been widely used to describe
locally interacting social or economic systems. We consider a related model,
introduced by Sznajd to describe the evolution of consensus in a society. In
this model, the opinion or state of any spins can only be changed through the
influence of neighbouring pairs of similarly aligned spins. Such pairs can
polarize their neighbours. We show that, assuming the global dynamics evolve in
a synchronous manner, the two-state Sznajd model exhibits a non-monotonically
decreasing overall orientation that has a maximum value when the system is
subject to a finite value of noise. Reinterpreting the model in terms of
opinions within a society we predict that consensus can be increased by the
addition of an appropriate amount of random noise. These features are explained
by the presence of islands of complete orientation that are stable in the
absence of noise but removed via the presence of added noise.Comment: 6 pages, 6 figure
Phase transitions, memory and frustration in a Sznajd-like model with synchronous updating
We introduce a consensus model inspired by the Sznajd Model. The updating is
synchronous and memory plays here a decisive role in making possible the
reaching of total consensus. We study the phase transition between the state
with no-consensus to the state with total consensus.Comment: to be published in the IJMP
Integriertes Praktikum am Beispiel einer thermoanalytischen Untersuchung der Kautschuk-Vulkanisation
Discontinuous Percolation Transitions in Epidemic Processes, Surface Depinning in Random Media and Hamiltonian Random Graphs
Discontinuous percolation transitions and the associated tricritical points
are manifest in a wide range of both equilibrium and non-equilibrium
cooperative phenomena. To demonstrate this, we present and relate the
continuous and first order behaviors in two different classes of models: The
first are generalized epidemic processes (GEP) that describe in their spatially
embedded version - either on or off a regular lattice - compact or fractal
cluster growth in random media at zero temperature. A random graph version of
GEP is mapped onto a model previously proposed for complex social contagion. We
compute detailed phase diagrams and compare our numerical results at the
tricritical point in d = 3 with field theory predictions of Janssen et al.
[Phys. Rev. E 70, 026114 (2004)]. The second class consists of exponential
("Hamiltonian", or formally equilibrium) random graph models and includes the
Strauss and the 2-star model, where 'chemical potentials' control the densities
of links, triangles or 2-stars. When the chemical potentials in either graph
model are O(logN), the percolation transition can coincide with a first order
phase transition in the density of links, making the former also discontinuous.
Hysteresis loops can then be of mixed order, with second order behavior for
decreasing link fugacity, and a jump (first order) when it increases
U.S. Geological Survey (USGS) Circum-Arctic Resource Appraisal: Estimates of Undiscovered Oil and Gas North of the Arctic Circle
Using a geology-based probabilistic methodology, the USGS estimated the occurrence
of undiscovered oil and gas in 33 geologic provinces thought to be prospective for petroleum. The sum of the mean estimates for each province indicates that 90 billion barrels of oil, 1,669 trillion cubic feet of natural gas, and 44 billion barrels of natural gas liquids may remain to be found in the Arctic, of which approximately
84 percent is expected to occur in offshore areas
Violating conformal invariance: Two-dimensional clusters grafted to wedges, cones, and branch points of Riemann surfaces
We present simulations of 2-d site animals on square and triangular lattices
in non-trivial geomeLattice animals are one of the few critical models in
statistical mechanics violating conformal invariance. We present here
simulations of 2-d site animals on square and triangular lattices in
non-trivial geometries. The simulations are done with the newly developed PERM
algorithm which gives very precise estimates of the partition sum, yielding
precise values for the entropic exponent (). In particular, we studied animals grafted to the tips of wedges
with a wide range of angles , to the tips of cones (wedges with the
sides glued together), and to branching points of Riemann surfaces. The latter
can either have sheets and no boundary, generalizing in this way cones to
angles degrees, or can have boundaries, generalizing wedges. We
find conformal invariance behavior, , only for small
angles (), while for
. These scalings hold both for wedges and cones. A heuristic
(non-conformal) argument for the behavior at large is given, and
comparison is made with critical percolation.Comment: 4 pages, includes 3 figure
Economic choices reveal probability distortion in macaque monkeys.
Economic choices are largely determined by two principal elements, reward value (utility) and probability. Although nonlinear utility functions have been acknowledged for centuries, nonlinear probability weighting (probability distortion) was only recently recognized as a ubiquitous aspect of real-world choice behavior. Even when outcome probabilities are known and acknowledged, human decision makers often overweight low probability outcomes and underweight high probability outcomes. Whereas recent studies measured utility functions and their corresponding neural correlates in monkeys, it is not known whether monkeys distort probability in a manner similar to humans. Therefore, we investigated economic choices in macaque monkeys for evidence of probability distortion. We trained two monkeys to predict reward from probabilistic gambles with constant outcome values (0.5 ml or nothing). The probability of winning was conveyed using explicit visual cues (sector stimuli). Choices between the gambles revealed that the monkeys used the explicit probability information to make meaningful decisions. Using these cues, we measured probability distortion from choices between the gambles and safe rewards. Parametric modeling of the choices revealed classic probability weighting functions with inverted-S shape. Therefore, the animals overweighted low probability rewards and underweighted high probability rewards. Empirical investigation of the behavior verified that the choices were best explained by a combination of nonlinear value and nonlinear probability distortion. Together, these results suggest that probability distortion may reflect evolutionarily preserved neuronal processing.This work was supported by the Wellcome Trust, European Research Council (ERC) and Caltech Conte Center.This is the final version of the article. It was first published by the Society for Neuroscience at http://www.jneurosci.org/content/35/7/3146.ful
Large-scale Simulation of the Two-dimensional Kinetic Ising Model
We present Monte Carlo simulation results for the dynamical critical exponent
of the two-dimensional kinetic Ising model using a lattice of size spins. We used Glauber as well as Metropolis dynamics. The
-value of was calculated from the magnetization and energy
relaxation from an ordered state towards the equilibrium state at .Comment: 6 pages + 2 figures as separate uuencoded compressed tar file,
Postscipt also available at http://wwwcp.tphys.uni-heidelberg.de/papers
Pair Connectedness and Shortest Path Scaling in Critical Percolation
We present high statistics data on the distribution of shortest path lengths
between two near-by points on the same cluster at the percolation threshold.
Our data are based on a new and very efficient algorithm. For they
clearly disprove a recent conjecture by M. Porto et al., Phys. Rev. {\bf E 58},
R5205 (1998). Our data also provide upper bounds on the probability that two
near-by points are on different infinite clusters.Comment: 7 pages, including 4 postscript figure
Random Sequential Renormalization of Networks I: Application to Critical Trees
We introduce the concept of Random Sequential Renormalization (RSR) for
arbitrary networks. RSR is a graph renormalization procedure that locally
aggregates nodes to produce a coarse grained network. It is analogous to the
(quasi-)parallel renormalization schemes introduced by C. Song {\it et al.}
(Nature {\bf 433}, 392 (2005)) and studied more recently by F. Radicchi {\it et
al.} (Phys. Rev. Lett. {\bf 101}, 148701 (2008)), but much simpler and easier
to implement. In this first paper we apply RSR to critical trees and derive
analytical results consistent with numerical simulations. Critical trees
exhibit three regimes in their evolution under RSR: (i) An initial regime
, where is the number of nodes at some step in the
renormalization and is the initial size. RSR in this regime is described
by a mean field theory and fluctuations from one realization to another are
small. The exponent is derived using random walk arguments. The
degree distribution becomes broader under successive renormalization --
reaching a power law, with and a variance
that diverges as at the end of this regime. Both of these results
are derived based on a scaling theory. (ii) An intermediate regime for
, in which hubs develop, and
fluctuations between different realizations of the RSR are large. Crossover
functions exhibiting finite size scaling, in the critical region , connect the behaviors in the first two regimes. (iii)
The last regime, for , is characterized by the
appearance of star configurations with a central hub surrounded by many leaves.
The distribution of sizes where stars first form is found numerically to be a
power law up to a cutoff that scales as with
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