1,308 research outputs found
Truncating the loop series expansion for Belief Propagation
Recently, M. Chertkov and V.Y. Chernyak derived an exact expression for the
partition sum (normalization constant) corresponding to a graphical model,
which is an expansion around the Belief Propagation solution. By adding
correction terms to the BP free energy, one for each "generalized loop" in the
factor graph, the exact partition sum is obtained. However, the usually
enormous number of generalized loops generally prohibits summation over all
correction terms. In this article we introduce Truncated Loop Series BP
(TLSBP), a particular way of truncating the loop series of M. Chertkov and V.Y.
Chernyak by considering generalized loops as compositions of simple loops. We
analyze the performance of TLSBP in different scenarios, including the Ising
model, regular random graphs and on Promedas, a large probabilistic medical
diagnostic system. We show that TLSBP often improves upon the accuracy of the
BP solution, at the expense of increased computation time. We also show that
the performance of TLSBP strongly depends on the degree of interaction between
the variables. For weak interactions, truncating the series leads to
significant improvements, whereas for strong interactions it can be
ineffective, even if a high number of terms is considered.Comment: 31 pages, 12 figures, submitted to Journal of Machine Learning
Researc
Superconductor-insulator transition in nanowires and nanowire arrays
Superconducting nanowires are the dual elements to Josephson junctions, with
quantum phase-slip processes replacing the tunneling of Cooper pairs. When the
quantum phase-slip amplitude ES is much smaller than the inductive energy EL,
the nanowire responds as a superconducting inductor. When the inductive energy
is small, the response is capacitive. The crossover at low temperatures as a
function of ES/EL is discussed and compared with earlier experimental results.
For one-dimensional and two-dimensional arrays of nanowires quantum phase
transitions are expected as a function of ES/EL. They can be tuned by a
homogeneous magnetic frustration.Comment: 15 pages, 10 figure
The merger of vertically offset quasi-geostrophic vortices
We examine the critical merging distance between two equal-volume, equal-potential-vorticity quasi-geostrophic vortices. We focus on how this distance depends on the vertical offset between the two vortices, each having a unit mean height-to-width aspect ratio. The vertical direction is special in the quasi-geostrophic model (used to capture the leading-order dynamical features of stably stratified and rapidly rotating geophysical flows) since vertical advection is absent. Nevertheless vortex merger may still occur by horizontal advection. In this paper, we first investigate the equilibrium states for the two vortices as a function of their vertical and horizontal separation. We examine their basic properties together with their linear stability. These findings are next compared to numerical simulations of the nonlinear evolution of two spheres of potential vorticity. Three different regimes of interaction are identified, depending on the vertical offset. For a small offset, the interaction differs little from the case when the two vortices are horizontally aligned. On the other hand, when the vertical offset is comparable to the mean vortex radius, strong interaction occurs for greater horizontal gaps than in the horizontally aligned case, and therefore at significantly greater full separation distances. This perhaps surprising result is consistent with the linear stability analysis and appears to be a consequence of the anisotropy of the quasi-geostrophic equations. Finally, for large vertical offsets, vortex merger results in the formation of a metastable tilted dumbbell vortex.Publisher PDFPeer reviewe
Phase-slip flux qubits
In thin superconducting wires, phase-slip by thermal activation near the
critical temperature is a well-known effect. It has recently become clear that
phase-slip by quantum tunnelling through the energy barrier can also have a
significant rate at low temperatures. In this paper it is suggested that
quantum phase-slip can be used to realize a superconducting quantum bit without
Josephson junctions. A loop containing a nanofabricated very thin wire is
biased with an externally applied magnetic flux of half a flux quantum,
resulting in two states with opposite circulating current and equal energy.
Quantum phase-slip should provide coherent coupling between these two
macroscopic states. Numbers are given for a wire of amorphous niobium-silicon
that can be fabricated with advanced electron beam lithography.Comment: Submitted to New Journal of Physics, special issue solid state
quantum informatio
Quantum transitions induced by the third cumulant of current fluctuations
We investigate the transitions induced by external current fluctuations on a
small probe quantum system. The rates for the transitions between the energy
states are calculated using the real-time Keldysh formalism for the density
matrix evolution. We especially detail the effects of the third cumulant of
current fluctuations inductively coupled to a quantum bit and propose a setup
for detecting the frequency-dependent third cumulant through the transitions it
induces.Comment: 4 pages, 3 figure
Statistical-mechanical iterative algorithms on complex networks
The Ising models have been applied for various problems on information
sciences, social sciences, and so on. In many cases, solving these problems
corresponds to minimizing the Bethe free energy. To minimize the Bethe free
energy, a statistical-mechanical iterative algorithm is often used. We study
the statistical-mechanical iterative algorithm on complex networks. To
investigate effects of heterogeneous structures on the iterative algorithm, we
introduce an iterative algorithm based on information of heterogeneity of
complex networks, in which higher-degree nodes are likely to be updated more
frequently than lower-degree ones. Numerical experiments clarified that the
usage of the information of heterogeneity affects the algorithm in BA networks,
but does not influence that in ER networks. It is revealed that information of
the whole system propagates rapidly through such high-degree nodes in the case
of Barab{\'a}si-Albert's scale-free networks.Comment: 7 pages, 6 figure
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