4,997 research outputs found
Traffic Control for Network Protection Against Spreading Processes
Epidemic outbreaks in human populations are facilitated by the underlying
transportation network. We consider strategies for containing a viral spreading
process by optimally allocating a limited budget to three types of protection
resources: (i) Traffic control resources, (ii), preventative resources and
(iii) corrective resources. Traffic control resources are employed to impose
restrictions on the traffic flowing across directed edges in the transportation
network. Preventative resources are allocated to nodes to reduce the
probability of infection at that node (e.g. vaccines), and corrective resources
are allocated to nodes to increase the recovery rate at that node (e.g.
antidotes). We assume these resources have monetary costs associated with them,
from which we formalize an optimal budget allocation problem which maximizes
containment of the infection. We present a polynomial time solution to the
optimal budget allocation problem using Geometric Programming (GP) for an
arbitrary weighted and directed contact network and a large class of resource
cost functions. We illustrate our approach by designing optimal traffic control
strategies to contain an epidemic outbreak that propagates through a real-world
air transportation network.Comment: arXiv admin note: text overlap with arXiv:1309.627
Kaleidoscope of exotic quantum phases in a frustrated XY model
The existence of quantum spin liquids was first conjectured by Pomeranchuk
some 70 years ago, who argued that frustration in simple antiferromagnetic
theories could result in a Fermi-liquid-like state for spinon excitations. Here
we show that a simple quantum spin model on a honeycomb lattice hosts the long
sought for Bose metal with a clearly identifiable Bose surface. The complete
phase diagram of the model is determined via exact diagonalization and is shown
to include four distinct phases separated by three quantum phase transitions
Some congruences involving central q-binomial coefficients
Motivated by recent works of Sun and Tauraso, we prove some variations on the
Green-Krammer identity involving central q-binomial coefficients, such as where is
the Legendre symbol and is the th cyclotomic polynomial. As
consequences, we deduce that \sum_{k=0}^{3^a m-1} q^{k}{2k\brack k}_q
&\equiv 0 \pmod{(1-q^{3^a})/(1-q)}, \sum_{k=0}^{5^a m-1}(-1)^kq^{-{k+1\choose
2}}{2k\brack k}_q &\equiv 0 \pmod{(1-q^{5^a})/(1-q)}, for , the
first one being a partial q-analogue of the Strauss-Shallit-Zagier congruence
modulo powers of 3. Several related conjectures are proposed.Comment: 16 pages, detailed proofs of Theorems 4.1 and 4.3 are added, to
appear in Adv. Appl. Mat
Stable topological phases in a family of two-dimensional fermion models
We show that a large class of two-dimensional spinless fermion models exhibit
topological superconducting phases characterized by a non-zero Chern number.
More specifically, we consider a generic one-band Hamiltonian of spinless
fermions that is invariant under both time-reversal, , and a group
of rotations and reflections, , which is either the dihedral
point-symmetry group of an underlying lattice, , or the
orthogonal group of rotations in continuum, . Pairing
symmetries are classified according to the irreducible representations of . We prove a theorem that for any two-dimensional
representation of this group, a time-reversal symmetry breaking paired state is
energetically favorable. This implies that the ground state of any spinless
fermion Hamiltonian in continuum or on a square lattice with a singly-connected
Fermi surface is always a topological superconductor in the presence of
attraction in at least one channel. Motivated by this discovery, we examine
phase diagrams of two specific lattice models with nearest-neighbor hopping and
attraction on a square lattice and a triangular lattice. In accordance with the
general theorem, the former model exhibits only a topological -wave
state, while the latter shows a doping-tuned quantum phase transition from such
state to a non-topological, but still exotic -wave superconductor.Comment: 6 pages, 2 figures, new references adde
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