1,536 research outputs found
Exact Statistical Characterization of Gram Matrices with Arbitrary Variance Profile
This paper is concerned with the statistical properties of the Gram matrix
, where is a
complex central Gaussian matrix whose elements have arbitrary variances. With
such arbitrary variance profile, this random matrix model fundamentally departs
from classical Wishart models and presents a significant challenge as the
classical analytical toolbox no longer directly applies. We derive new exact
expressions for the distribution of and that of its eigenvalues by
means of an explicit parameterization of the group of unitary matrices. Our
results yield remarkably simple expressions, which are further leveraged to
study the outage data rate of a dual-antenna communication system under
different variance profiles.Comment: 6 pages, 1 figure, 1 tabl
Scalable Online Betweenness Centrality in Evolving Graphs
Betweenness centrality is a classic measure that quantifies the importance of
a graph element (vertex or edge) according to the fraction of shortest paths
passing through it. This measure is notoriously expensive to compute, and the
best known algorithm runs in O(nm) time. The problems of efficiency and
scalability are exacerbated in a dynamic setting, where the input is an
evolving graph seen edge by edge, and the goal is to keep the betweenness
centrality up to date. In this paper we propose the first truly scalable
algorithm for online computation of betweenness centrality of both vertices and
edges in an evolving graph where new edges are added and existing edges are
removed. Our algorithm is carefully engineered with out-of-core techniques and
tailored for modern parallel stream processing engines that run on clusters of
shared-nothing commodity hardware. Hence, it is amenable to real-world
deployment. We experiment on graphs that are two orders of magnitude larger
than previous studies. Our method is able to keep the betweenness centrality
measures up to date online, i.e., the time to update the measures is smaller
than the inter-arrival time between two consecutive updates.Comment: 15 pages, 9 Figures, accepted for publication in IEEE Transactions on
Knowledge and Data Engineerin
When Two Choices Are not Enough: Balancing at Scale in Distributed Stream Processing
Carefully balancing load in distributed stream processing systems has a
fundamental impact on execution latency and throughput. Load balancing is
challenging because real-world workloads are skewed: some tuples in the stream
are associated to keys which are significantly more frequent than others. Skew
is remarkably more problematic in large deployments: more workers implies fewer
keys per worker, so it becomes harder to "average out" the cost of hot keys
with cold keys.
We propose a novel load balancing technique that uses a heaving hitter
algorithm to efficiently identify the hottest keys in the stream. These hot
keys are assigned to choices to ensure a balanced load, where is
tuned automatically to minimize the memory and computation cost of operator
replication. The technique works online and does not require the use of routing
tables. Our extensive evaluation shows that our technique can balance
real-world workloads on large deployments, and improve throughput and latency
by and respectively over the previous
state-of-the-art when deployed on Apache Storm.Comment: 12 pages, 14 Figures, this paper is accepted and will be published at
ICDE 201
Lunar impact flashes from Geminids, analysis of luminous efficiencies and the flux of large meteoroids on Earth
We analyze lunar impact flashes recorded by our team during runs in December
2007, 2011, 2013 and 2014. In total, 12 impact flashes with magnitudes ranging
between 7.1 and 9.3 in V band were identified. From these, 9 events could be
linked to the Geminid stream. Using these observations the ratio of luminous
energy emitted in the flashes with respect to the kinetic energy of the
impactors for meteoroids of the Geminid stream is estimated. By making use of
the known Geminids meteoroid flux on Earth we found this ratio to be
2.1x10 on average. We compare this luminous efficiency with other
estimations derived in the past for other meteoroid streams and also compare it
with other estimations that we present here for the first time by making use of
crater diameter measurements. We think that the luminous efficiency has to be
revised downward, not upward, at least for sporadic impacts. This implies an
increase in the influx of kilogram-sized and larger bodies on Earth that has
been derived thus far through the lunar impact flash monitoring technique
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