48,038 research outputs found
Degree Distribution of Competition-Induced Preferential Attachment Graphs
We introduce a family of one-dimensional geometric growth models, constructed
iteratively by locally optimizing the tradeoffs between two competing metrics,
and show that this family is equivalent to a family of preferential attachment
random graph models with upper cutoffs. This is the first explanation of how
preferential attachment can arise from a more basic underlying mechanism of
local competition. We rigorously determine the degree distribution for the
family of random graph models, showing that it obeys a power law up to a finite
threshold and decays exponentially above this threshold.
We also rigorously analyze a generalized version of our graph process, with
two natural parameters, one corresponding to the cutoff and the other a
``fertility'' parameter. We prove that the general model has a power-law degree
distribution up to a cutoff, and establish monotonicity of the power as a
function of the two parameters. Limiting cases of the general model include the
standard preferential attachment model without cutoff and the uniform
attachment model.Comment: 24 pages, one figure. To appear in the journal: Combinatorics,
Probability and Computing. Note, this is a long version, with complete
proofs, of the paper "Competition-Induced Preferential Attachment"
(cond-mat/0402268
From Koszul duality to Poincar\'e duality
We discuss the notion of Poincar\'e duality for graded algebras and its
connections with the Koszul duality for quadratic Koszul algebras. The
relevance of the Poincar\'e duality is pointed out for the existence of twisted
potentials associated to Koszul algebras as well as for the extraction of a
good generalization of Lie algebras among the quadratic-linear algebras.Comment: Dedicated to Raymond Stora. 27 page
On the push&pull protocol for rumour spreading
The asynchronous push&pull protocol, a randomized distributed algorithm for
spreading a rumour in a graph , works as follows. Independent Poisson clocks
of rate 1 are associated with the vertices of . Initially, one vertex of
knows the rumour. Whenever the clock of a vertex rings, it calls a random
neighbour : if knows the rumour and does not, then tells the
rumour (a push operation), and if does not know the rumour and knows
it, tells the rumour (a pull operation). The average spread time of
is the expected time it takes for all vertices to know the rumour, and the
guaranteed spread time of is the smallest time such that with
probability at least , after time all vertices know the rumour. The
synchronous variant of this protocol, in which each clock rings precisely at
times , has been studied extensively. We prove the following results
for any -vertex graph: In either version, the average spread time is at most
linear even if only the pull operation is used, and the guaranteed spread time
is within a logarithmic factor of the average spread time, so it is . In the asynchronous version, both the average and guaranteed spread times
are . We give examples of graphs illustrating that these bounds
are best possible up to constant factors. We also prove theoretical
relationships between the guaranteed spread times in the two versions. Firstly,
in all graphs the guaranteed spread time in the asynchronous version is within
an factor of that in the synchronous version, and this is tight.
Next, we find examples of graphs whose asynchronous spread times are
logarithmic, but the synchronous versions are polynomially large. Finally, we
show for any graph that the ratio of the synchronous spread time to the
asynchronous spread time is .Comment: 25 page
Spatio-Temporal Scaling of Solar Surface Flows
The Sun provides an excellent natural laboratory for nonlinear phenomena. We
use motions of magnetic bright points on the solar surface, at the smallest
scales yet observed, to study the small scale dynamics of the photospheric
plasma. The paths of the bright points are analyzed within a continuous time
random walk framework. Their spatial and temporal scaling suggest that the
observed motions are the walks of imperfectly correlated tracers on a turbulent
fluid flow in the lanes between granular convection cells.Comment: Now Accepted by Physical Review Letter
Thiadizoloquinoxaline-Based Low-Bandgap Conjugated Polymers as Ambipolar Semiconductors for Organic Field Effect Transistors
A New Constraint on the Escape Fraction in Distant Galaxies Using Gamma-ray Burst Afterglow Spectroscopy
We describe a new method to measure the escape fraction fesc of ionizing
radiation from distant star-forming galaxies using the afterglow spectra of
long-duration gamma-ray bursts (GRBs). Optical spectra of GRB afterglows allow
us to evaluate the optical depth of the host ISM, according to the neutral
hydrogen column density N(HI) observed along the sightlines toward the
star-forming regions where the GRBs are found. Different from previous effort
in searching for faint, transmitted Lyman continuum photons, our method is not
subject to background subtraction uncertainties and does not require prior
knowledge of either the spectral shape of the host galaxy population or the IGM
Lya forest absorption along these GRB sightlines. Because most GRBs occur in
sub-L_* galaxies, our study also offers the first constraint on fesc for
distant low-mass galaxies that dominate the cosmic luminosity density. We have
compiled a sample of 27 GRBs at redshift z>2 for which the underlying N(HI) in
the host ISM are known. These GRBs together offer a statistical sampling of the
integrated optical depth to ionizing photons along random sightlines from
star-forming regions in the host galaxies, and allow us to estimate the mean
escape fraction averaged over different viewing angles. We find
=0.02\pm 0.02 and place a 95% c.l. upper limit <= 0.075 for these
hosts. We discuss possible biases of our approach and implications of the
result. Finally, we propose to extend this technique for measuring at
z~0.2 using spectra of core-collapse supernovae.Comment: Five journal pages, including one figure; ApJL in pres
Revealing the role of electrons and phonons in the ultrafast recovery of charge density wave correlations in 1-TiSe
Using time- and angle-resolved photoemission spectroscopy with selective
near- and mid-infrared photon excitations, we investigate the femtosecond
dynamics of the charge density wave (CDW) phase in 1-TiSe, as well as
the dynamics of CDW fluctuations at 240 K. In the CDW phase, we observe the
coherent oscillation of the CDW amplitude mode. At 240 K, we single out an
ultrafast component in the recovery of the CDW correlations, which we explain
as the manifestation of electron-hole correlations. Our momentum-resolved study
of femtosecond electron dynamics supports a mechanism for the CDW phase
resulting from the cooperation between the interband Coulomb interaction, the
mechanism of excitonic insulator phase formation, and electron-phonon coupling.Comment: 9 pages, 6 figure
Chromospheric Variability in SDSS M Dwarfs. II. Short-Timescale H-alpha Variability
[Abridged] We present the first comprehensive study of short-timescale
chromospheric H-alpha variability in M dwarfs using the individual 15 min
spectroscopic exposures for 52,392 objects from the Sloan Digital Sky Survey.
Our sample contains about 10^3-10^4 objects per spectral type bin in the range
M0-M9, with a total of about 206,000 spectra and a typical number of 3
exposures per object (ranging up to a maximum of 30 exposures). Using this
extensive data set we find that about 16% of the sources exhibit H-alpha
emission in at least one exposure, and of those about 45% exhibit H-alpha
emission in all of the available exposures. Within the sample of objects with
H-alpha emission, only 26% are consistent with non-variable emission,
independent of spectral type. The H-alpha variability, quantified in terms of
the ratio of maximum to minimum H-alpha equivalent width (R_EW), and the ratio
of the standard deviation to the mean (sigma_EW/), exhibits a rapid rise
from M0 to M5, followed by a plateau and a possible decline in M9 objects. In
particular, R_EW increases from a median value of about 1.8 for M0-M3 to about
2.5 for M7-M9, and variability with R_EW>10 is only observed in objects later
than M5. For the combined sample we find that the R_EW values follow an
exponential distribution with N(R_EW) exp[-(R_EW-1)/2]; for M5-M9 objects the
characteristic scale is R_EW-1\approx 2.7, indicative of stronger variability.
In addition, we find that objects with persistent H-alpha emission exhibit
smaller values of R_EW than those with intermittent H-alpha emission. Based on
these results we conclude that H-alpha variability in M dwarfs on timescales of
15 min to 1 hr increases with later spectral type, and that the variability is
larger for intermittent sources.Comment: Submitted to ApJ; 20 pages, 15 figure
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