142 research outputs found
Growing Networks: Limit in-degree distribution for arbitrary out-degree one
We compute the stationary in-degree probability, , for a growing
network model with directed edges and arbitrary out-degree probability. In
particular, under preferential linking, we find that if the nodes have a light
tail (finite variance) out-degree distribution, then the corresponding
in-degree one behaves as . Moreover, for an out-degree distribution
with a scale invariant tail, , the corresponding
in-degree distribution has exactly the same asymptotic behavior only if
(infinite variance). Similar results are obtained when
attractiveness is included. We also present some results on descriptive
statistics measures %descriptive statistics such as the correlation between the
number of in-going links, , and outgoing links, , and the
conditional expectation of given , and we calculate these
measures for the WWW network. Finally, we present an application to the
scientific publications network. The results presented here can explain the
tail behavior of in/out-degree distribution observed in many real networks.Comment: 12 pages, 6 figures, v2 adds a section on descriptive statistics, an
analisis on www network, typos adde
Retrieving the structure of probabilistic sequences of auditory stimuli from EEG data
Using a new probabilistic approach we model the relationship between
sequences of auditory stimuli generated by stochastic chains and the
electroencephalographic (EEG) data acquired while 19 participants were exposed
to those stimuli. The structure of the chains generating the stimuli are
characterized by rooted and labeled trees whose leaves, henceforth called
contexts, represent the sequences of past stimuli governing the choice of the
next stimulus. A classical conjecture claims that the brain assigns
probabilistic models to samples of stimuli. If this is true, then the context
tree generating the sequence of stimuli should be encoded in the brain
activity. Using an innovative statistical procedure we show that this context
tree can effectively be extracted from the EEG data, thus giving support to the
classical conjecture.Comment: 16 pages, 7 figure
Collapse of solitary waves near transition from supercritical to subcritical bifurcations
We study both analytically and numerically the nonlinear stage of the
instability of one-dimensional solitons in a small vicinity of the transition
point from supercritical to subcritical bifurcations in the framework of the
generalized nonlinear Schr\"{o}dinger equation. It is shown that near the
collapsing time the pulse amplitude and its width demonstrate the self-similar
behavior with a small asymmetry at the pulse tails due to self-steepening. This
theory is applied to both solitary interfacial deep-water waves and envelope
water waves with a finite depth and short optical pulses in fibers as well
Emergent complex neural dynamics
A large repertoire of spatiotemporal activity patterns in the brain is the
basis for adaptive behaviour. Understanding the mechanism by which the brain's
hundred billion neurons and hundred trillion synapses manage to produce such a
range of cortical configurations in a flexible manner remains a fundamental
problem in neuroscience. One plausible solution is the involvement of universal
mechanisms of emergent complex phenomena evident in dynamical systems poised
near a critical point of a second-order phase transition. We review recent
theoretical and empirical results supporting the notion that the brain is
naturally poised near criticality, as well as its implications for better
understanding of the brain
Ultrashort filaments of light in weakly-ionized, optically-transparent media
Modern laser sources nowadays deliver ultrashort light pulses reaching few
cycles in duration, high energies beyond the Joule level and peak powers
exceeding several terawatt (TW). When such pulses propagate through
optically-transparent media, they first self-focus in space and grow in
intensity, until they generate a tenuous plasma by photo-ionization. For free
electron densities and beam intensities below their breakdown limits, these
pulses evolve as self-guided objects, resulting from successive equilibria
between the Kerr focusing process, the chromatic dispersion of the medium, and
the defocusing action of the electron plasma. Discovered one decade ago, this
self-channeling mechanism reveals a new physics, widely extending the frontiers
of nonlinear optics. Implications include long-distance propagation of TW beams
in the atmosphere, supercontinuum emission, pulse shortening as well as
high-order harmonic generation. This review presents the landmarks of the
10-odd-year progress in this field. Particular emphasis is laid to the
theoretical modeling of the propagation equations, whose physical ingredients
are discussed from numerical simulations. Differences between femtosecond
pulses propagating in gaseous or condensed materials are underlined. Attention
is also paid to the multifilamentation instability of broad, powerful beams,
breaking up the energy distribution into small-scale cells along the optical
path. The robustness of the resulting filaments in adverse weathers, their
large conical emission exploited for multipollutant remote sensing, nonlinear
spectroscopy, and the possibility to guide electric discharges in air are
finally addressed on the basis of experimental results.Comment: 50 pages, 38 figure
Epithelioid Angiosarcoma of the Small Intestine After Occupational Exposure to Radiation and Polyvinyl Chloride: A case Report and Review of Literature
Angiosarcomas represent 1–2% of soft tissue sarcomas and most frequently occur in the subcutis. They may affect internal
organs, such as the heart, liver, and spleen, and only rarely do they emerge in the gastrointestinal tract. The association
between angiosarcomas and certain toxic chemical substances or previous external-beam radiation therapy is well
documented
A novel brain partition highlights the modular skeleton shared by structure and function
Elucidating the intricate relationship between brain structure and function, both in healthy and pathological conditions, is a key challenge for modern neuroscience. Recent progress in neuroimaging has helped advance our understanding of this important issue, with diffusion images providing information about structural connectivity (SC) and functional magnetic resonance imaging shedding light on resting state functional connectivity (rsFC). Here, we adopt a systems approach, relying on modular hierarchical clustering, to study together SC and rsFC datasets gathered independently from healthy human subjects. Our novel approach allows us to find a common skeleton shared by structure and function from which a new, optimal, brain partition can be extracted. We describe the emerging common structure-function modules (SFMs) in detail and compare them with commonly employed anatomical or functional parcellations. Our results underline the strong correspondence between brain structure and resting-state dynamics as well as the emerging coherent organization of the human brain.Work supported by Ikerbasque: The Basque Foundation for Science, Euskampus at UPV/EHU, Gobierno Vasco (Saiotek SAIO13-PE13BF001) and Junta de AndalucÃa (P09-FQM-4682) to JMC; Ikerbasque Visiting Professor to SS; Junta de AndalucÃa (P09-FQM-4682) and Spanish Ministry of Economy and Competitiveness (FIS2013-43201-P) to MAM; the European Union’s Seventh Framework Programme (ICT-FET FP7/2007-2013, FET Young Explorers scheme) under grant agreement n. 284772 BRAIN BOW (www.brainbowproject.eu) and by the Joint Italy—Israel Laboratory on Neuroscience to PB. For results validation (figure S8), data were provided by the Human Connectome Project, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research; and by the McDonnell Center for Systems Neuroscience at Washington University
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