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 $G$, the fine structure constant $\alpha$, and a composite parameter $C$ 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

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

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