27,648 research outputs found
Transport in networks with multiple sources and sinks
We investigate the electrical current and flow (number of parallel paths)
between two sets of n sources and n sinks in complex networks. We derive
analytical formulas for the average current and flow as a function of n. We
show that for small n, increasing n improves the total transport in the
network, while for large n bottlenecks begin to form. For the case of flow,
this leads to an optimal n* above which the transport is less efficient. For
current, the typical decrease in the length of the connecting paths for large n
compensates for the effect of the bottlenecks. We also derive an expression for
the average flow as a function of n under the common limitation that transport
takes place between specific pairs of sources and sinks
Tracking multiple sediment cascades at the river network scale identifies controls and emerging patterns of sediment connectivity
Sediment connectivity in fluvial networks results from the transfer of sediment between multiple
sources and sinks. Connectivity scales differently between all sources and sinks as a function of distance,
source grain size and sediment supply, network topology and topography, and hydrologic forcing. In this
paper, we address the challenge of quantifying sediment connectivity and its controls at the network scale.
We expand the concept of a single, catchment-scale sediment cascade toward representing sediment transport
from each source as a suite of individual cascading processes. We implement this approach in the
herein presented CAtchment Sediment Connectivity And DElivery (CASCADE) modeling framework. In CASCADE,
each sediment cascade establishes connectivity between a specific source and its multiple sinks.
From a source perspective, the fate of sediment is controlled by its detachment and downstream transport
capacity, resulting in a specific trajectory of transfer and deposition. From a sink perspective, the assemblage
of incoming cascades defines provenance, sorting, and magnitude of sediment deliveries. At the network
scale, this information reveals emerging patterns of connectivity and the location of bottlenecks,
where disconnectivity occurs. In this paper, we apply CASCADE to quantitatively analyze the sediment connectivity
of a major river system in SE Asia. The approach provides a screening model that can support analyses
of large, poorly monitored river systems. We test the sensitivity of CASCADE to various parameters and
identify the distribution of energy between the multiple, simultaneously active sediment cascades as key
control behind network sediment connectivity. To conclude, CASCADE enables a quantitative, spatially
explicit analysis of network sediment connectivity with potential applications in both river science and
management
Multi-Source Multi-Sink Nash Flows over Time
Nash flows over time describe the behavior of selfish users eager to reach their destination as early as possible while traveling along the arcs of a network with capacities and transit times. Throughout the past decade, they have been thoroughly studied in single-source single-sink networks for the deterministic queuing model, which is of particular relevance and frequently used in the context of traffic and transport networks. In this setting there exist Nash flows over time that can be described by a sequence of static flows featuring special properties, so-called `thin flows with resetting\u27. This insight can also be used algorithmically to compute Nash flows over time. We present an extension of these results to networks with multiple sources and sinks which are much more relevant in practical applications. In particular, we come up with a subtle generalization of thin flows with resetting, which yields a compact description as well as an algorithmic approach for computing multi-terminal Nash flows over time
Transport of multiple users in complex networks
We study the transport properties of model networks such as scale-free and
Erd\H{o}s-R\'{e}nyi networks as well as a real network. We consider the
conductance between two arbitrarily chosen nodes where each link has the
same unit resistance. Our theoretical analysis for scale-free networks predicts
a broad range of values of , with a power-law tail distribution , where , and is the decay
exponent for the scale-free network degree distribution. We confirm our
predictions by large scale simulations. The power-law tail in leads to large values of , thereby significantly improving the
transport in scale-free networks, compared to Erd\H{o}s-R\'{e}nyi networks
where the tail of the conductivity distribution decays exponentially. We
develop a simple physical picture of the transport to account for the results.
We study another model for transport, the \emph{max-flow} model, where
conductance is defined as the number of link-independent paths between the two
nodes, and find that a similar picture holds. The effects of distance on the
value of conductance are considered for both models, and some differences
emerge. We then extend our study to the case of multiple sources, where the
transport is define between two \emph{groups} of nodes. We find a fundamental
difference between the two forms of flow when considering the quality of the
transport with respect to the number of sources, and find an optimal number of
sources, or users, for the max-flow case. A qualitative (and partially
quantitative) explanation is also given
General analytical solutions for DC/AC circuit-network analysis
All authors thank the Scottish University Physics Alliance (SUPA) support. NR also acknowledges de support of PEDECIBA, Uruguay. MSB acknowledges the support of EPSRC grant Ref. EP/I032606/1. Open access via Springer Compact Agreement.Peer reviewedPublisher PD
Resiliently evolving supply-demand networks
Peer reviewedPublisher PD
Networked Slepian-Wolf: theory, algorithms, and scaling laws
Consider a set of correlated sources located at the nodes of a network, and a set of sinks that are the destinations for some of the sources. The minimization of cost functions which are the product of a function of the rate and a function of the path weight is considered, for both the data-gathering scenario, which is relevant in sensor networks, and general traffic matrices, relevant for general networks. The minimization is achieved by jointly optimizing a) the transmission structure, which is shown to consist in general of a superposition of trees, and b) the rate allocation across the source nodes, which is done by Slepian-Wolf coding. The overall minimization can be achieved in two concatenated steps. First, the optimal transmission structure is found, which in general amounts to finding a Steiner tree, and second, the optimal rate allocation is obtained by solving an optimization problem with cost weights determined by the given optimal transmission structure, and with linear constraints given by the Slepian-Wolf rate region. For the case of data gathering, the optimal transmission structure is fully characterized and a closed-form solution for the optimal rate allocation is provided. For the general case of an arbitrary traffic matrix, the problem of finding the optimal transmission structure is NP-complete. For large networks, in some simplified scenarios, the total costs associated with Slepian-Wolf coding and explicit communication (conditional encoding based on explicitly communicated side information) are compared. Finally, the design of decentralized algorithms for the optimal rate allocation is analyzed
Algorithms for Constructing Overlay Networks For Live Streaming
We present a polynomial time approximation algorithm for constructing an
overlay multicast network for streaming live media events over the Internet.
The class of overlay networks constructed by our algorithm include networks
used by Akamai Technologies to deliver live media events to a global audience
with high fidelity. We construct networks consisting of three stages of nodes.
The nodes in the first stage are the entry points that act as sources for the
live streams. Each source forwards each of its streams to one or more nodes in
the second stage that are called reflectors. A reflector can split an incoming
stream into multiple identical outgoing streams, which are then sent on to
nodes in the third and final stage that act as sinks and are located in edge
networks near end-users. As the packets in a stream travel from one stage to
the next, some of them may be lost. A sink combines the packets from multiple
instances of the same stream (by reordering packets and discarding duplicates)
to form a single instance of the stream with minimal loss. Our primary
contribution is an algorithm that constructs an overlay network that provably
satisfies capacity and reliability constraints to within a constant factor of
optimal, and minimizes cost to within a logarithmic factor of optimal. Further
in the common case where only the transmission costs are minimized, we show
that our algorithm produces a solution that has cost within a factor of 2 of
optimal. We also implement our algorithm and evaluate it on realistic traces
derived from Akamai's live streaming network. Our empirical results show that
our algorithm can be used to efficiently construct large-scale overlay networks
in practice with near-optimal cost
Transitions from trees to cycles in adaptive flow networks
Transport networks are crucial to the functioning of natural and
technological systems. Nature features transport networks that are adaptive
over a vast range of parameters, thus providing an impressive level of
robustness in supply. Theoretical and experimental studies have found that
real-world transport networks exhibit both tree-like motifs and cycles. When
the network is subject to load fluctuations, the presence of cyclic motifs may
help to reduce flow fluctuations and, thus, render supply in the network more
robust. While previous studies considered network topology via optimization
principles, here, we take a dynamical systems approach and study a simple model
of a flow network with dynamically adapting weights (conductances). We assume a
spatially non-uniform distribution of rapidly fluctuating loads in the sinks
and investigate what network configurations are dynamically stable. The network
converges to a spatially non-uniform stable configuration composed of both
cyclic and tree-like structures. Cyclic structures emerge locally in a
transcritical bifurcation as the amplitude of the load fluctuations is
increased. The resulting adaptive dynamics thus partitions the network into two
distinct regions with cyclic and tree-like structures. The location of the
boundary between these two regions is determined by the amplitude of the
fluctuations. These findings may explain why natural transport networks display
cyclic structures in the micro-vascular regions near terminal nodes, but
tree-like features in the regions with larger veins
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