2,220 research outputs found
Auxiliary field approach to dilute Bose gases with tunable interactions
We rewrite the Lagrangian for a dilute Bose gas in terms of auxiliary fields
related to the normal and anomalous condensate densities. We derive the loop
expansion of the effective action in the composite-field propagators. The
lowest-order auxiliary field (LOAF) theory is a conserving mean-field
approximation consistent with the Goldstone theorem without some of the
difficulties plaguing approximations such as the Hartree and Popov
approximations. LOAF predicts a second-order phase transition. We give a set of
Feynman rules for improving results to any order in the loop expansion in terms
of composite-field propagators. We compare results of the LOAF approximation
with those derived using the Popov approximation. LOAF allows us to explore the
critical regime for all values of the coupling constant and we determine
various parameters in the unitarity limit.Comment: 16 pages, 7 figure
Evaluating Local Community Methods in Networks
We present a new benchmarking procedure that is unambiguous and specific to
local community-finding methods, allowing one to compare the accuracy of
various methods. We apply this to new and existing algorithms. A simple class
of synthetic benchmark networks is also developed, capable of testing
properties specific to these local methods.Comment: 8 pages, 9 figures, code included with sourc
Stars In Other Universes: Stellar structure with different fundamental constants
Motivated by the possible existence of other universes, with possible
variations in the laws of physics, this paper explores the parameter space of
fundamental constants that allows for the existence of stars. To make this
problem tractable, we develop a semi-analytical stellar structure model that
allows for physical understanding of these stars with unconventional
parameters, as well as a means to survey the relevant parameter space. In this
work, the most important quantities that determine stellar properties -- and
are allowed to vary -- are the gravitational constant , the fine structure
constant , and a composite parameter that determines nuclear
reaction rates. Working within this model, we delineate the portion of
parameter space that allows for the existence of stars. Our main finding is
that a sizable fraction of the parameter space (roughly one fourth) provides
the values necessary for stellar objects to operate through sustained nuclear
fusion. As a result, the set of parameters necessary to support stars are not
particularly rare. In addition, we briefly consider the possibility that
unconventional stars (e.g., black holes, dark matter stars) play the role
filled by stars in our universe and constrain the allowed parameter space.Comment: accepted to JCAP, 29 pages, 6 figure
The Asymptotic Form of Cosmic Structure: Small Scale Power and Accretion History
We explore the effects of small scale structure on the formation and
equilibrium of dark matter halos in a universe dominated by vacuum energy. We
present the results of a suite of four N-body simulations, two with a LCDM
initial power spectrum and two with WDM-like spectra that suppress the early
formation of small structures. All simulations are run into to far future when
the universe is 64Gyr/h old, long enough for halos to essentially reach
dynamical equilibrium. We quantify the importance of hierarchical merging on
the halo mass accretion history, the substructure population, and the
equilibrium density profile. We modify the mass accretion history function of
Wechsler et al. (2002) by introducing a parameter, \gamma, that controls the
rate of mass accretion, dln(M) / dln(a) ~ a^(-\gamma), and find that this form
characterizes both hierarchical and monolithic formation. Subhalo decay rates
are exponential in time with a much shorter time scale for WDM halos. At the
end of the simulations, we find truncated Hernquist density profiles for halos
in both the CDM and WDM cosmologies. There is a systematic shift to lower
concentration for WDM halos, but both cosmologies lie on the same locus
relating concentration and formation epoch. Because the form of the density
profile remains unchanged, our results indicate that the equilibrium halo
density profile is set independently of the halo formation process.Comment: 17 pages, submitted to ApJ. Full resolution version avaliable at
http://www-personal.umich.edu/~mbusha/Papers/AccretionHistory.pd
Landscape natural resources management using forage grasses and legume intercrops
United States Agency for International Developmen
Comparing community structure identification
We compare recent approaches to community structure identification in terms
of sensitivity and computational cost. The recently proposed modularity measure
is revisited and the performance of the methods as applied to ad hoc networks
with known community structure, is compared. We find that the most accurate
methods tend to be more computationally expensive, and that both aspects need
to be considered when choosing a method for practical purposes. The work is
intended as an introduction as well as a proposal for a standard benchmark test
of community detection methods.Comment: 10 pages, 3 figures, 1 table. v2: condensed, updated version as
appears in JSTA
Local multiresolution order in community detection
Community detection algorithms attempt to find the best clusters of nodes in
an arbitrary complex network. Multi-scale ("multiresolution") community
detection extends the problem to identify the best network scale(s) for these
clusters. The latter task is generally accomplished by analyzing community
stability simultaneously for all clusters in the network. In the current work,
we extend this general approach to define local multiresolution methods, which
enable the extraction of well-defined local communities even if the global
community structure is vaguely defined in an average sense. Toward this end, we
propose measures analogous to variation of information and normalized mutual
information that are used to quantitatively identify the best resolution(s) at
the community level based on correlations between clusters in
independently-solved systems. We demonstrate our method on two constructed
networks as well as a real network and draw inferences about local community
strength. Our approach is independent of the applied community detection
algorithm save for the inherent requirement that the method be able to identify
communities across different network scales, with appropriate changes to
account for how different resolutions are evaluated or defined in a particular
community detection method. It should, in principle, easily adapt to
alternative community comparison measures.Comment: 19 pages, 11 figure
Positive and Negative Evidence Accumulation Clustering for Sensor Fusion: An Application to Heartbeat Clustering
In this work, a new clustering algorithm especially geared towards merging data arising from multiple sensors is presented. The algorithm, called PN-EAC, is based on the ensemble clustering paradigm and it introduces the novel concept of negative evidence. PN-EAC combines both positive evidence, to gather information about the elements that should be grouped together in the final partition, and negative evidence, which has information about the elements that should not be grouped together. The algorithm has been validated in the electrocardiographic domain for heartbeat clustering, extracting positive evidence from the heartbeat morphology and negative evidence from the distances between heartbeats. The best result obtained on the MIT-BIH Arrhythmia database yielded an error of 1.44%. In the St. Petersburg Institute of Cardiological Technics 12-Lead Arrhythmia Database database (INCARTDB), an error of 0.601% was obtained when using two electrocardiogram (ECG) leads. When increasing the number of leads to 4, 6, 8, 10 and 12, the algorithm obtains better results (statistically significant) than with the previous number of leads, reaching an error of 0.338%. To the best of our knowledge, this is the first clustering algorithm that is able to process simultaneously any number of ECG leads. Our results support the use of PN-EAC to combine different sources of information and the value of the negative evidenceThis research was funded by the Ministry of Science, Innovation and Universities of Spain, and the European Regional Development Fund of the European Commission, Grant Nos. RTI2018-095324-B-I00, RTI2018-097122-A-I00, and RTI2018-099646-B-I00S
Finding overlapping communities in networks by label propagation
We propose an algorithm for finding overlapping community structure in very
large networks. The algorithm is based on the label propagation technique of
Raghavan, Albert, and Kumara, but is able to detect communities that overlap.
Like the original algorithm, vertices have labels that propagate between
neighbouring vertices so that members of a community reach a consensus on their
community membership. Our main contribution is to extend the label and
propagation step to include information about more than one community: each
vertex can now belong to up to v communities, where v is the parameter of the
algorithm. Our algorithm can also handle weighted and bipartite networks. Tests
on an independently designed set of benchmarks, and on real networks, show the
algorithm to be highly effective in recovering overlapping communities. It is
also very fast and can process very large and dense networks in a short time
Modes of Multiple Star Formation
This paper argues that star forming environments should be classified into
finer divisions than the traditional isolated and clustered modes. Using the
observed set of galactic open clusters and theoretical considerations regarding
cluster formation, we estimate the fraction of star formation that takes place
within clusters. We find that less than 10% of the stellar population
originates from star forming regions destined to become open clusters,
confirming earlier estimates. The smallest clusters included in the
observational surveys (having at least N=100 members) roughly coincide with the
smallest stellar systems that are expected to evolve as clusters in a dynamical
sense. We show that stellar systems with too few members N < N_\star have
dynamical relaxation times that are shorter than their formation times (1-2
Myr), where the critical number of stars N_\star \approx 100. Our results
suggest that star formation can be characterized by (at least) three principal
modes: I. isolated singles and binaries, II. groups (N<N_\star), and III.
clusters (N>N_\star). Many -- if not most -- stars form through the
intermediate mode in stellar groups with 10<N<100. Such groups evolve and
disperse much more rapidly than open clusters; groups also have a low
probability of containing massive stars and are unaffected by supernovae and
intense ultraviolet radiation fields. Because of their short lifetimes and
small stellar membership, groups have relatively little effect on the star
formation process (on average) compared to larger open clusters.Comment: accepted to The Astrophysical Journa
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