15,680 research outputs found
STEPS - an approach for human mobility modeling
In this paper we introduce Spatio-TEmporal Parametric Stepping (STEPS) - a simple parametric mobility model which can cover a large spectrum of human mobility patterns. STEPS makes abstraction of spatio-temporal preferences in human mobility by using a power law to rule the nodes movement. Nodes in STEPS have preferential attachment to favorite locations where they spend most of their time. Via simulations, we show that STEPS is able, not only to express the peer to peer properties such as inter-ontact/contact time and to reflect accurately realistic routing performance, but also to express the structural properties of the underlying interaction graph such as small-world phenomenon. Moreover, STEPS is easy to implement, exible to configure and also theoretically tractable
Adiabatic quantum algorithm for search engine ranking
We propose an adiabatic quantum algorithm for generating a quantum pure state
encoding of the PageRank vector, the most widely used tool in ranking the
relative importance of internet pages. We present extensive numerical
simulations which provide evidence that this algorithm can prepare the quantum
PageRank state in a time which, on average, scales polylogarithmically in the
number of webpages. We argue that the main topological feature of the
underlying web graph allowing for such a scaling is the out-degree
distribution. The top ranked entries of the quantum PageRank state
can then be estimated with a polynomial quantum speedup. Moreover, the quantum
PageRank state can be used in "q-sampling" protocols for testing properties of
distributions, which require exponentially fewer measurements than all
classical schemes designed for the same task. This can be used to decide
whether to run a classical update of the PageRank.Comment: 7 pages, 5 figures; closer to published versio
Local majority dynamics on preferential attachment graphs
Suppose in a graph vertices can be either red or blue. Let be odd. At
each time step, each vertex in polls random neighbours and takes
the majority colour. If it doesn't have neighbours, it simply polls all of
them, or all less one if the degree of is even. We study this protocol on
the preferential attachment model of Albert and Barab\'asi, which gives rise to
a degree distribution that has roughly power-law ,
as well as generalisations which give exponents larger than . The setting is
as follows: Initially each vertex of is red independently with probability
, and is otherwise blue. We show that if is
sufficiently biased away from , then with high probability,
consensus is reached on the initial global majority within
steps. Here is the number of vertices and is the minimum of
and (or if is even), being the number of edges each new
vertex adds in the preferential attachment generative process. Additionally,
our analysis reduces the required bias of for graphs of a given degree
sequence studied by the first author (which includes, e.g., random regular
graphs)
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