120,429 research outputs found
D-brane networks in flux vacua, generalized cycles and calibrations
We consider chains of generalized submanifolds, as defined by Gualtieri in
the context of generalized complex geometry, and define a boundary operator
that acts on them. This allows us to define generalized cycles and the
corresponding homology theory. Gauge invariance demands that D-brane networks
on flux vacua must wrap these generalized cycles, while deformations of
generalized cycles inside of a certain homology class describe physical
processes such as the dissolution of D-branes in higher-dimensional D-branes
and MMS-like instantonic transitions. We introduce calibrations that identify
the supersymmetric D-brane networks, which minimize their energy inside of the
corresponding homology class of generalized cycles. Such a calibration is
explicitly presented for type II N=1 flux compactifications to four dimensions.
In particular networks of walls and strings in compactifications on warped
Calabi-Yau's are treated, with explicit examples on a toroidal orientifold
vacuum and on the Klebanov-Strassler geometry.Comment: 42 pages, 4 eps figures, version to appear in JHE
Clustering in Complex Directed Networks
Many empirical networks display an inherent tendency to cluster, i.e. to form
circles of connected nodes. This feature is typically measured by the
clustering coefficient (CC). The CC, originally introduced for binary,
undirected graphs, has been recently generalized to weighted, undirected
networks. Here we extend the CC to the case of (binary and weighted) directed
networks and we compute its expected value for random graphs. We distinguish
between CCs that count all directed triangles in the graph (independently of
the direction of their edges) and CCs that only consider particular types of
directed triangles (e.g., cycles). The main concepts are illustrated by
employing empirical data on world-trade flows
Unidirectional Quorum-based Cycle Planning for Efficient Resource Utilization and Fault-Tolerance
In this paper, we propose a greedy cycle direction heuristic to improve the
generalized redundancy quorum cycle technique. When applied using
only single cycles rather than the standard paired cycles, the generalized
redundancy technique has been shown to almost halve the necessary
light-trail resources in the network. Our greedy heuristic improves this
cycle-based routing technique's fault-tolerance and dependability.
For efficiency and distributed control, it is common in distributed systems
and algorithms to group nodes into intersecting sets referred to as quorum
sets. Optimal communication quorum sets forming optical cycles based on
light-trails have been shown to flexibly and efficiently route both
point-to-point and multipoint-to-multipoint traffic requests. Commonly cycle
routing techniques will use pairs of cycles to achieve both routing and
fault-tolerance, which uses substantial resources and creates the potential for
underutilization. Instead, we use a single cycle and intentionally utilize
redundancy within the quorum cycles such that every point-to-point
communication pairs occur in at least cycles. Without the paired
cycles the direction of the quorum cycles becomes critical to the fault
tolerance performance. For this we developed a greedy cycle direction heuristic
and our single fault network simulations show a reduction of missing pairs by
greater than 30%, which translates to significant improvements in fault
coverage.Comment: Computer Communication and Networks (ICCCN), 2016 25th International
Conference on. arXiv admin note: substantial text overlap with
arXiv:1608.05172, arXiv:1608.05168, arXiv:1608.0517
The Kuramoto model on oriented and signed graphs
Many real-world systems of coupled agents exhibit directed interactions,
meaning that the influence of an agent on another is not reciprocal.
Furthermore, interactions usually do not have identical amplitude and/or sign.
To describe synchronization phenomena in such systems, we use a generalized
Kuramoto model with oriented, weighted and signed interactions. Taking a
bottom-up approach, we investigate the simplest possible oriented networks,
namely acyclic oriented networks and oriented cycles. These two types of
networks are fundamental building blocks from which many general oriented
networks can be constructed. For acyclic, weighted and signed networks, we are
able to completely characterize synchronization properties through necessary
and sufficient conditions, which we show are optimal. Additionally, we prove
that if it exists, a stable synchronous state is unique. In oriented, weighted
and signed cycles with identical natural frequencies, we show that the system
globally synchronizes and that the number of stable synchronous states is
finite.Comment: 20 pages, 9 figure
Clustering in large networks does not promote upstream reciprocity
Upstream reciprocity (also called generalized reciprocity) is a putative
mechanism for cooperation in social dilemma situations with which players help
others when they are helped by somebody else. It is a type of indirect
reciprocity. Although upstream reciprocity is often observed in experiments,
most theories suggest that it is operative only when players form short cycles
such as triangles, implying a small population size, or when it is combined
with other mechanisms that promote cooperation on their own. An expectation is
that real social networks, which are known to be full of triangles and other
short cycles, may accommodate upstream reciprocity. In this study, I extend the
upstream reciprocity game proposed for a directed cycle by Boyd and Richerson
to the case of general networks. The model is not evolutionary and concerns the
conditions under which the unanimity of cooperative players is a Nash
equilibrium. I show that an abundance of triangles or other short cycles in a
network does little to promote upstream reciprocity. Cooperation is less likely
for a larger population size even if triangles are abundant in the network. In
addition, in contrast to the results for evolutionary social dilemma games on
networks, scale-free networks lead to less cooperation than networks with a
homogeneous degree distribution.Comment: 5 figure
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