22,982 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
The Theory of Caustics and Wavefront Singularities with Physical Applications
This is intended as an introduction to and review of the work of V, Arnold
and his collaborators on the theory of Lagrangian and Legendrian submanifolds
and their associated maps. The theory is illustrated by applications to
Hamilton-Jacobi theory and the eikonal equation, with an emphasis on null
surfaces and wavefronts and their associated caustics and singularities.Comment: Figs. not include
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
The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles
We analyze the global structure of the world-wide air transportation network,
a critical infrastructure with an enormous impact on local, national, and
international economies. We find that the world-wide air transportation network
is a scale-free small-world network. In contrast to the prediction of
scale-free network models, however, we find that the most connected cities are
not necessarily the most central, resulting in anomalous values of the
centrality. We demonstrate that these anomalies arise because of the
multi-community structure of the network. We identify the communities in the
air transportation network and show that the community structure cannot be
explained solely based on geographical constraints, and that geo-political
considerations have to be taken into account. We identify each city's global
role based on its pattern of inter- and intra-community connections, which
enables us to obtain scale-specific representations of the network.Comment: Revised versio
The 4-D Layer Phase as a Gauge Field Localization: Extensive Study of the 5-D Anisotropic U(1) Gauge Model on the Lattice
We study a 4+1 dimensional pure Abelian Gauge model on the lattice with two
anisotropic couplings independent of each other and of the coordinates. A first
exploration of the phase diagram using mean field approximation and monte carlo
techniques has demonstrated the existence of a new phase, the so called Layer
phase, in which the forces in the 4-D subspace are Coulomb-like while in the
transverse direction (fifth dimension) the force is confining. This allows the
possibility of a gauge field localization scheme. In this work the use of
bigger lattice volumes and higher statistics confirms the existence of the
Layer phase and furthermore clarifies the issue of the phase transitions'
order. We show that the Layer phase is separated from the strongly coupled
phase by a weak first order phase transition. Also we provide evidence that the
Layer phase is separated by the five-dimensional Coulomb phase with a second
order phase transition and we give a first estimation of the critical
exponents.Comment: 19 pages, 16 figure
Fuchsian analysis of singularities in Gowdy spacetimes beyond analyticity
Fuchsian equations provide a way of constructing large classes of spacetimes
whose singularities can be described in detail. In some of the applications of
this technique only the analytic case could be handled up to now. This paper
develops a method of removing the undesirable hypothesis of analyticity. This
is applied to the specific case of the Gowdy spacetimes in order to show that
analogues of the results known in the analytic case hold in the smooth case. As
far as possible the likely strengths and weaknesses of the method as applied to
more general problems are displayed.Comment: 14 page
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.
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
Detecting rich-club ordering in complex networks
Uncovering the hidden regularities and organizational principles of networks
arising in physical systems ranging from the molecular level to the scale of
large communication infrastructures is the key issue for the understanding of
their fabric and dynamical properties [1-5]. The ``rich-club'' phenomenon
refers to the tendency of nodes with high centrality, the dominant elements of
the system, to form tightly interconnected communities and it is one of the
crucial properties accounting for the formation of dominant communities in both
computer and social sciences [4-8]. Here we provide the analytical expression
and the correct null models which allow for a quantitative discussion of the
rich-club phenomenon. The presented analysis enables the measurement of the
rich-club ordering and its relation with the function and dynamics of networks
in examples drawn from the biological, social and technological domains.Comment: 1 table, 3 figure
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