3,334 research outputs found
Distinguishing Infections on Different Graph Topologies
The history of infections and epidemics holds famous examples where
understanding, containing and ultimately treating an outbreak began with
understanding its mode of spread. Influenza, HIV and most computer viruses,
spread person to person, device to device, through contact networks; Cholera,
Cancer, and seasonal allergies, on the other hand, do not. In this paper we
study two fundamental questions of detection: first, given a snapshot view of a
(perhaps vanishingly small) fraction of those infected, under what conditions
is an epidemic spreading via contact (e.g., Influenza), distinguishable from a
"random illness" operating independently of any contact network (e.g., seasonal
allergies); second, if we do have an epidemic, under what conditions is it
possible to determine which network of interactions is the main cause of the
spread -- the causative network -- without any knowledge of the epidemic, other
than the identity of a minuscule subsample of infected nodes?
The core, therefore, of this paper, is to obtain an understanding of the
diagnostic power of network information. We derive sufficient conditions
networks must satisfy for these problems to be identifiable, and produce
efficient, highly scalable algorithms that solve these problems. We show that
the identifiability condition we give is fairly mild, and in particular, is
satisfied by two common graph topologies: the grid, and the Erdos-Renyi graphs
Continuous-time quantum walks on one-dimension regular networks
In this paper, we consider continuous-time quantum walks (CTQWs) on
one-dimension ring lattice of N nodes in which every node is connected to its
2m nearest neighbors (m on either side). In the framework of the Bloch function
ansatz, we calculate the spacetime transition probabilities between two nodes
of the lattice. We find that the transport of CTQWs between two different nodes
is faster than that of the classical continuous-time random walk (CTRWs). The
transport speed, which is defined by the ratio of the shortest path length and
propagating time, increases with the connectivity parameter m for both the
CTQWs and CTRWs. For fixed parameter m, the transport of CTRWs gets slow with
the increase of the shortest distance while the transport (speed) of CTQWs
turns out to be a constant value. In the long time limit, depending on the
network size N and connectivity parameter m, the limiting probability
distributions of CTQWs show various paterns. When the network size N is an even
number, the probability of being at the original node differs from that of
being at the opposite node, which also depends on the precise value of
parameter m.Comment: Typos corrected and Phys. ReV. E comments considered in this versio
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