631 research outputs found
Learning about knowledge: A complex network approach
This article describes an approach to modeling knowledge acquisition in terms
of walks along complex networks. Each subset of knowledge is represented as a
node, and relations between such knowledge are expressed as edges. Two types of
edges are considered, corresponding to free and conditional transitions. The
latter case implies that a node can only be reached after visiting previously a
set of nodes (the required conditions). The process of knowledge acquisition
can then be simulated by considering the number of nodes visited as a single
agent moves along the network, starting from its lowest layer. It is shown that
hierarchical networks, i.e. networks composed of successive interconnected
layers, arise naturally as a consequence of compositions of the prerequisite
relationships between the nodes. In order to avoid deadlocks, i.e. unreachable
nodes, the subnetwork in each layer is assumed to be a connected component.
Several configurations of such hierarchical knowledge networks are simulated
and the performance of the moving agent quantified in terms of the percentage
of visited nodes after each movement. The Barab\'asi-Albert and random models
are considered for the layer and interconnecting subnetworks. Although all
subnetworks in each realization have the same number of nodes, several
interconnectivities, defined by the average node degree of the interconnection
networks, have been considered. Two visiting strategies are investigated:
random choice among the existing edges and preferential choice to so far
untracked edges. A series of interesting results are obtained, including the
identification of a series of plateaux of knowledge stagnation in the case of
the preferential movements strategy in presence of conditional edges.Comment: 18 pages, 19 figure
Average shape of fluctuations for subdiffusive walks
We study the average shape of fluctuations for subdiffusive processes, i.e.,
processes with uncorrelated increments but where the waiting time distribution
has a broad power-law tail. This shape is obtained analytically by means of a
fractional diffusion approach. We find that, in contrast with processes where
the waiting time between increments has finite variance, the fluctuation shape
is no longer a semicircle: it tends to adopt a table-like form as the
subdiffusive character of the process increases. The theoretical predictions
are compared with numerical simulation results.Comment: 4 pages, 6 figures. Accepted for publication Phys. Rev. E (Replaced
for the latest version, in press.) Section II rewritte
Collaboration in sensor network research: an in-depth longitudinal analysis of assortative mixing patterns
Many investigations of scientific collaboration are based on statistical
analyses of large networks constructed from bibliographic repositories. These
investigations often rely on a wealth of bibliographic data, but very little or
no other information about the individuals in the network, and thus, fail to
illustrate the broader social and academic landscape in which collaboration
takes place. In this article, we perform an in-depth longitudinal analysis of a
relatively small network of scientific collaboration (N = 291) constructed from
the bibliographic record of a research center involved in the development and
application of sensor network and wireless technologies. We perform a
preliminary analysis of selected structural properties of the network,
computing its range, configuration and topology. We then support our
preliminary statistical analysis with an in-depth temporal investigation of the
assortative mixing of selected node characteristics, unveiling the researchers'
propensity to collaborate preferentially with others with a similar academic
profile. Our qualitative analysis of mixing patterns offers clues as to the
nature of the scientific community being modeled in relation to its
organizational, disciplinary, institutional, and international arrangements of
collaboration.Comment: Scientometrics (In press
Anomalous accelerations in spacecraft flybys of the Earth
[EN] The flyby anomaly is a persistent riddle in astrodynamics.
Orbital analysis in several flybys of the Earth
since the Galileo spacecraft flyby of the Earth in 1990 have
shown that the asymptotic post-encounter velocity exhibits
a difference with the initial velocity that cannot be attributed
to conventional effects. To elucidate its origin, we have developed
an orbital program for analyzing the trajectory of
the spacecraft in the vicinity of the perigee, including both
the Sun and the MoonÂżs tidal perturbations and the geopotential
zonal, tesseral and sectorial harmonics provided by
the EGM96 model. The magnitude and direction of the
anomalous acceleration acting upon the spacecraft can be
estimated from the orbital determination program by comparing
with the trajectories fitted to telemetry data as provided
by the mission teams. This acceleration amounts to a
fraction of a mm/s2 and decays very fast with altitude. The
possibility of some new physics of gravity in the altitude
range for spacecraft flybys is discussed.Acedo RodrĂguez, L. (2017). Anomalous accelerations in spacecraft flybys of the Earth. Astrophysics and Space Science. 362(12):1-15. doi:10.1007/s10509-017-3205-xS11536212Acedo, L.: Galaxies 3, 113 (2015)Acedo, L.: Mon. Not. R. Astron. Soc. 463(2), 2119 (2016)Acedo, L.: Adv. Space Res. 59(7), 1715 (2017). 1701.06939Acedo, L., Bel, L.: Astron. Nachr. 338(1), 117 (2017). 1602.03669Adler, S.L.: Int. J. Mod. Phys. A 25, 4577 (2010). 0908.2414 . doi: 10.1142/S0217751X10050706Adler, S.L.: In: Proceedings of the Conference in Honour of Murray Gellimannâs 80th Birthday, p. 352 (2011). doi: 10.1142/9789814335614_0032Anderson, J.D., Nieto, M.M.: In: Klioner, S.A., Seidelmann, P.K., Soffel, M.H. (eds.) Relativity in Fundamental Astronomy: Dynamics, Reference Frames, and Data Analysis. IAU Symposium, vol. 261, p. 189 (2010). doi: 10.1017/S1743921309990378Anderson, J.D., Laing, P.A., Lau, E.L., Liu, A.S., Nieto, M.M., Turyshev, S.G.: Phys. Rev. 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Order statistics of the trapping problem
When a large number N of independent diffusing particles are placed upon a
site of a d-dimensional Euclidean lattice randomly occupied by a concentration
c of traps, what is the m-th moment of the time t_{j,N} elapsed
until the first j are trapped? An exact answer is given in terms of the
probability Phi_M(t) that no particle of an initial set of M=N, N-1,..., N-j
particles is trapped by time t. The Rosenstock approximation is used to
evaluate Phi_M(t), and it is found that for a large range of trap
concentracions the m-th moment of t_{j,N} goes as x^{-m} and its variance as
x^{-2}, x being ln^{2/d} (1-c) ln N. A rigorous asymptotic expression (dominant
and two corrective terms) is given for for the one-dimensional
lattice.Comment: 11 pages, 7 figures, to be published in Phys. Rev.
Reaction Front in an A+B -> C Reaction-Subdiffusion Process
We study the reaction front for the process A+B -> C in which the reagents
move subdiffusively. Our theoretical description is based on a fractional
reaction-subdiffusion equation in which both the motion and the reaction terms
are affected by the subdiffusive character of the process. We design numerical
simulations to check our theoretical results, describing the simulations in
some detail because the rules necessarily differ in important respects from
those used in diffusive processes. Comparisons between theory and simulations
are on the whole favorable, with the most difficult quantities to capture being
those that involve very small numbers of particles. In particular, we analyze
the total number of product particles, the width of the depletion zone, the
production profile of product and its width, as well as the reactant
concentrations at the center of the reaction zone, all as a function of time.
We also analyze the shape of the product profile as a function of time, in
particular its unusual behavior at the center of the reaction zone
Random Convex Hulls and Extreme Value Statistics
In this paper we study the statistical properties of convex hulls of
random points in a plane chosen according to a given distribution. The points
may be chosen independently or they may be correlated. After a non-exhaustive
survey of the somewhat sporadic literature and diverse methods used in the
random convex hull problem, we present a unifying approach, based on the notion
of support function of a closed curve and the associated Cauchy's formulae,
that allows us to compute exactly the mean perimeter and the mean area enclosed
by the convex polygon both in case of independent as well as correlated points.
Our method demonstrates a beautiful link between the random convex hull problem
and the subject of extreme value statistics. As an example of correlated
points, we study here in detail the case when the points represent the vertices
of independent random walks. In the continuum time limit this reduces to
independent planar Brownian trajectories for which we compute exactly, for
all , the mean perimeter and the mean area of their global convex hull. Our
results have relevant applications in ecology in estimating the home range of a
herd of animals. Some of these results were announced recently in a short
communication [Phys. Rev. Lett. {\bf 103}, 140602 (2009)].Comment: 61 pages (pedagogical review); invited contribution to the special
issue of J. Stat. Phys. celebrating the 50 years of Yeshiba/Rutgers meeting
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