24,470 research outputs found
Speciational view of macroevolution: are micro and macroevolution decoupled?
We introduce a simple computational model that, with a microscopic dynamics
driven by natural selection and mutation alone, allows the description of true
speciation events. A statistical analysis of the so generated evolutionary tree
captures realistic features showing power laws for frequency distributions in
time and size. Albeit these successful predictions, the difficulty in obtaining
punctuated dynamics with mass extinctions suggests the necessity of decoupling
micro and macro-evolutionary mechanisms in agreement with some ideas of Gould's
and Eldredge's theory of punctuated equilibrium.Comment: Europhys. Lett. 75:342--34
Multi-beam Energy Moments of Multibeam Particle Velocity Distributions
High resolution electron and ion velocity distributions, f(v), which consist
of N effectively disjoint beams, have been measured by NASA's Magnetospheric
Multi-Scale Mission (MMS) observatories and in reconnection simulations.
Commonly used standard velocity moments generally assume a single
mean-flow-velocity for the entire distribution, which can lead to
counterintuitive results for a multibeam f(v). An example is the (false)
standard thermal energy moment of a pair of equal and opposite cold particle
beams, which is nonzero even though each beam has zero thermal energy. By
contrast, a multibeam moment of two or more beams has no false thermal energy.
A multibeam moment is obtained by taking a standard moment of each beam and
then summing over beams. In this paper we will generalize these notions,
explore their consequences and apply them to an f(v) which is sum of
tri-Maxwellians. Both standard and multibeam energy moments have coherent and
incoherent forms. Examples of incoherent moments are the thermal energy
density, the pressure and the thermal energy flux (enthalpy flux plus heat
flux). Corresponding coherent moments are the bulk kinetic energy density, the
RAM pressure and the bulk kinetic energy flux. The false part of an incoherent
moment is defined as the difference between the standard incoherent moment and
the corresponding multibeam moment. The sum of a pair of corresponding coherent
and incoherent moments will be called the undecomposed moment. Undecomposed
moments are independent of whether the sum is standard or multibeam and
therefore have advantages when studying moments of measured f(v).Comment: 27 single-spaced pages. Three Figure
Characterizing the structure of small-world networks
We give exact relations which are valid for small-world networks (SWN's) with
a general `degree distribution', i.e the distribution of nearest-neighbor
connections. For the original SWN model, we illustrate how these exact
relations can be used to obtain approximations for the corresponding basic
probability distribution. In the limit of large system sizes and small
disorder, we use numerical studies to obtain a functional fit for this
distribution. Finally, we obtain the scaling properties for the mean-square
displacement of a random walker, which are determined by the scaling behavior
of the underlying SWN
Graph Metrics for Temporal Networks
Temporal networks, i.e., networks in which the interactions among a set of
elementary units change over time, can be modelled in terms of time-varying
graphs, which are time-ordered sequences of graphs over a set of nodes. In such
graphs, the concepts of node adjacency and reachability crucially depend on the
exact temporal ordering of the links. Consequently, all the concepts and
metrics proposed and used for the characterisation of static complex networks
have to be redefined or appropriately extended to time-varying graphs, in order
to take into account the effects of time ordering on causality. In this chapter
we discuss how to represent temporal networks and we review the definitions of
walks, paths, connectedness and connected components valid for graphs in which
the links fluctuate over time. We then focus on temporal node-node distance,
and we discuss how to characterise link persistence and the temporal
small-world behaviour in this class of networks. Finally, we discuss the
extension of classic centrality measures, including closeness, betweenness and
spectral centrality, to the case of time-varying graphs, and we review the work
on temporal motifs analysis and the definition of modularity for temporal
graphs.Comment: 26 pages, 5 figures, Chapter in Temporal Networks (Petter Holme and
Jari Saram\"aki editors). Springer. Berlin, Heidelberg 201
Wang-Landau Algorithm: a Theoretical Analysis of the Saturation of the Error
In this work we present a theoretical analysis of the convergence of the
Wang-Landau algorithm [Phys. Rev. Lett. 86, 2050 (2001)] which was introduced
years ago to calculate the density of states in statistical models. We study
the dynamical behavior of the error in the calculation of the density of
states.We conclude that the source of the saturation of the error is due to the
decreasing variations of the refinement parameter. To overcome this limitation,
we present an analytical treatment in which the refinement parameter is scaled
down as a power law instead of exponentially. An extension of the analysis to
the N-fold way variation of the method is also discussed.Comment: 7 pages, 5 figure
Why social networks are different from other types of networks
We argue that social networks differ from most other types of networks,
including technological and biological networks, in two important ways. First,
they have non-trivial clustering or network transitivity, and second, they show
positive correlations, also called assortative mixing, between the degrees of
adjacent vertices. Social networks are often divided into groups or
communities, and it has recently been suggested that this division could
account for the observed clustering. We demonstrate that group structure in
networks can also account for degree correlations. We show using a simple model
that we should expect assortative mixing in such networks whenever there is
variation in the sizes of the groups and that the predicted level of
assortative mixing compares well with that observed in real-world networks.Comment: 9 pages, 2 figure
Nonequilibrium phase transition in surface growth
Conserved growth models that exhibit a nonlinear instability in which the
height (depth) of isolated pillars (grooves) grows in time are studied by
numerical integration and stochastic simulation. When this instability is
controlled by the introduction of an infinite series of higher-order nonlinear
terms, these models exhibit, as function of a control parameter, a
non-equilibrium phase transition between a kinetically rough phase with
self-affine scaling and a phase that exhibits mound formation, slope selection
and power-law coarsening.Comment: 7 pages, 4 .eps figures (Minor changes in text and references.
Critical Behavior of an Ising System on the Sierpinski Carpet: A Short-Time Dynamics Study
The short-time dynamic evolution of an Ising model embedded in an infinitely
ramified fractal structure with noninteger Hausdorff dimension was studied
using Monte Carlo simulations. Completely ordered and disordered spin
configurations were used as initial states for the dynamic simulations. In both
cases, the evolution of the physical observables follows a power-law behavior.
Based on this fact, the complete set of critical exponents characteristic of a
second-order phase transition was evaluated. Also, the dynamic exponent of the critical initial increase in magnetization, as well as the critical
temperature, were computed. The exponent exhibits a weak dependence
on the initial (small) magnetization. On the other hand, the dynamic exponent
shows a systematic decrease when the segmentation step is increased, i.e.,
when the system size becomes larger. Our results suggest that the effective
noninteger dimension for the second-order phase transition is noticeably
smaller than the Hausdorff dimension. Even when the behavior of the
magnetization (in the case of the ordered initial state) and the
autocorrelation (in the case of the disordered initial state) with time are
very well fitted by power laws, the precision of our simulations allows us to
detect the presence of a soft oscillation of the same type in both magnitudes
that we attribute to the topological details of the generating cell at any
scale.Comment: 10 figures, 4 tables and 14 page
Small-World Networks: Links with long-tailed distributions
Small-world networks (SWN), obtained by randomly adding to a regular
structure additional links (AL), are of current interest. In this article we
explore (based on physical models) a new variant of SWN, in which the
probability of realizing an AL depends on the chemical distance between the
connected sites. We assume a power-law probability distribution and study
random walkers on the network, focussing especially on their probability of
being at the origin. We connect the results to L\'evy Flights, which follow
from a mean field variant of our model.Comment: 11 pages, 4 figures, to appear in Phys.Rev.
Topological Effects caused by the Fractal Substrate on the Nonequilibrium Critical Behavior of the Ising Magnet
The nonequilibrium critical dynamics of the Ising magnet on a fractal
substrate, namely the Sierpinski carpet with Hausdorff dimension =1.7925,
has been studied within the short-time regime by means of Monte Carlo
simulations. The evolution of the physical observables was followed at
criticality, after both annealing ordered spin configurations (ground state)
and quenching disordered initial configurations (high temperature state), for
three segmentation steps of the fractal. The topological effects become evident
from the emergence of a logarithmic periodic oscillation superimposed to a
power law in the decay of the magnetization and its logarithmic derivative and
also from the dependence of the critical exponents on the segmentation step.
These oscillations are discussed in the framework of the discrete scale
invariance of the substrate and carefully characterized in order to determine
the critical temperature of the second-order phase transition and the critical
exponents corresponding to the short-time regime. The exponent of the
initial increase in the magnetization was also obtained and the results suggest
that it would be almost independent of the fractal dimension of the susbstrate,
provided that is close enough to d=2.Comment: 9 figures, 3 tables, 10 page
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