7,094 research outputs found
Parallel algorithms and concentration bounds for the Lovasz Local Lemma via witness DAGs
The Lov\'{a}sz Local Lemma (LLL) is a cornerstone principle in the
probabilistic method of combinatorics, and a seminal algorithm of Moser &
Tardos (2010) provides an efficient randomized algorithm to implement it. This
can be parallelized to give an algorithm that uses polynomially many processors
and runs in time on an EREW PRAM, stemming from
adaptive computations of a maximal independent set (MIS). Chung et al. (2014)
developed faster local and parallel algorithms, potentially running in time
, but these algorithms require more stringent conditions than the
LLL.
We give a new parallel algorithm that works under essentially the same
conditions as the original algorithm of Moser & Tardos but uses only a single
MIS computation, thus running in time on an EREW PRAM. This can
be derandomized to give an NC algorithm running in time as well,
speeding up a previous NC LLL algorithm of Chandrasekaran et al. (2013).
We also provide improved and tighter bounds on the run-times of the
sequential and parallel resampling-based algorithms originally developed by
Moser & Tardos. These apply to any problem instance in which the tighter
Shearer LLL criterion is satisfied
Uncovering the Temporal Dynamics of Diffusion Networks
Time plays an essential role in the diffusion of information, influence and
disease over networks. In many cases we only observe when a node copies
information, makes a decision or becomes infected -- but the connectivity,
transmission rates between nodes and transmission sources are unknown.
Inferring the underlying dynamics is of outstanding interest since it enables
forecasting, influencing and retarding infections, broadly construed. To this
end, we model diffusion processes as discrete networks of continuous temporal
processes occurring at different rates. Given cascade data -- observed
infection times of nodes -- we infer the edges of the global diffusion network
and estimate the transmission rates of each edge that best explain the observed
data. The optimization problem is convex. The model naturally (without
heuristics) imposes sparse solutions and requires no parameter tuning. The
problem decouples into a collection of independent smaller problems, thus
scaling easily to networks on the order of hundreds of thousands of nodes.
Experiments on real and synthetic data show that our algorithm both recovers
the edges of diffusion networks and accurately estimates their transmission
rates from cascade data.Comment: To appear in the 28th International Conference on Machine Learning
(ICML), 2011. Website: http://www.stanford.edu/~manuelgr/netrate
Increased variability of microbial communities in restored salt marshes nearly 30 years after tidal flow restoration
We analyzed microbial diversity and community composition from four salt marsh sites that were impounded for 40–50 years and subsequently restored and four unimpounded sites in southeastern Connecticut over one growing season. Community composition and diversity were assessed by terminal restriction fragment length polymorphism (TRFLP) and sequence analysis of 16S ribosomal RNA (rRNA) genes. Our results indicated diverse communities, with sequences representing 14 different bacterial divisions. Proteobacteria, Bacteroidetes, and Planctomycetes dominated clone libraries from both restored and unimpounded sites. Multivariate analysis of the TRFLP data suggest significant site, sample date, and restoration status effects, but the exact causes of these effects are not clear. Composition of clone libraries and abundance of bacterial 16S rRNA genes were not significantly different between restored sites and unimpounded sites, but restored sites showed greater temporal and spatial variability of bacterial communities based on TRFLP profiles compared with unimpounded sites, and variability was greatest at sites more recently restored. In summary, our study suggests there may be long-lasting effects on stability of bacterial communities in restored salt marshes and raises questions about the resilience and ultimate recovery of the communities after chronic disturbance
Gambling Alone? A Study of Solitary and Social Gambling in America
In his acclaimed 2000 book Bowling Alone, Robert Putnam documents a disturbing social trend of the broadest kind. Putnam cites a wide variety of data that indicate that over the past fifty years, Americans have become increasingly socially disengaged. In developing this theme, Putnam specifically cites the increase in casino gambling (and especially machine gambling) as evidence in support of his argument. Building on the empirical and theoretical work of Putnam, this exploratory article examines the subphenomenon of gambling alone by exploring sample survey data on solitary and social gambling behavior among adults who reside in Las Vegas, Nevada. Specifically, to further understand these phenomena, a number of demographic, attitudinal, and behavioral variables are examined for their explanatory power in predicting solitary vs. social gambling behavior
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