179 research outputs found
A Comparative Study of Matrix Factorization and Random Walk with Restart in Recommender Systems
Between matrix factorization or Random Walk with Restart (RWR), which method
works better for recommender systems? Which method handles explicit or implicit
feedback data better? Does additional information help recommendation?
Recommender systems play an important role in many e-commerce services such as
Amazon and Netflix to recommend new items to a user. Among various
recommendation strategies, collaborative filtering has shown good performance
by using rating patterns of users. Matrix factorization and random walk with
restart are the most representative collaborative filtering methods. However,
it is still unclear which method provides better recommendation performance
despite their extensive utility.
In this paper, we provide a comparative study of matrix factorization and RWR
in recommender systems. We exactly formulate each correspondence of the two
methods according to various tasks in recommendation. Especially, we newly
devise an RWR method using global bias term which corresponds to a matrix
factorization method using biases. We describe details of the two methods in
various aspects of recommendation quality such as how those methods handle
cold-start problem which typically happens in collaborative filtering. We
extensively perform experiments over real-world datasets to evaluate the
performance of each method in terms of various measures. We observe that matrix
factorization performs better with explicit feedback ratings while RWR is
better with implicit ones. We also observe that exploiting global popularities
of items is advantageous in the performance and that side information produces
positive synergy with explicit feedback but gives negative effects with
implicit one.Comment: 10 pages, Appears in IEEE International Conference on Big Data 2017
(IEEE BigData 2017
Topological dephasing in the fractional Quantum Hall Regime
We study dephasing in electron transport through a large quantum dot (a
Fabry-Perot interferometer) in the fractional quantum Hall regime with filling
factor . In the regime of sequential tunneling, dephasing occurs due to
electron fractionalization into counterpropagating charge and neutral edge
modes on the dot. In particular, when the charge mode moves much faster than
the neutral mode, and at temperatures higher than the level spacing of the dot,
electron fractionalization combined with tje fractional statistics of the
charge mode leads to the dephasing selectively suppressing Aharonov-Bohm
oscillations but not oscillations, resulting in oscillation-period
halving.Comment: 11pages, 3 figure
Incoherent transport on the quantum Hall edge
The nature of edge state transport in quantum Hall systems has been studied
intensely ever since Halperin [1] noted its importance for the quantization of
the Hall conductance. Since then, there have been many developments in the
study of edge states in the quantum Hall effect, including the prediction of
multiple counter-propagating modes in the fractional quantum Hall regime, the
prediction of edge mode renormalization due to disorder, and studies of how the
sample confining potential affects the edge state structure (edge
reconstruction), among others. In this paper, we study edge transport for the
edge in the disordered, fully incoherent transport
regime. To do so, we use a hydrodynamic approximation for the calculation of
voltage and temperature profiles along the edge of the sample. Within this
formalism, we study two different bare mode structures with tunneling: the
original edge structure predicted by Wen [2] and MacDonald [3], and the more
complicated edge structure proposed by Meir [4], whose renormalization and
transport characteristics were discussed by Wang, Meir and Gefen (WMG) [5]. We
find that in the fully incoherent regime, the topological characteristics of
transport (quantized electrical and heat conductance) are intact, with finite
size corrections which are determined by the extent of equilibration. In
particular, our calculation of conductance for the WMG model in a double QPC
geometry reproduce conductance results of a recent experiment by R. Sabo, et
al. [17], which are inconsistent with the model of MacDonald. Our results can
be explained in the charge/neutral mode picture, with incoherent analogues of
the renormalization fixed points of Ref. [5]. Additionally, we find diffusive
conductivity corrections to the heat conductance in the fully
incoherent regime for both models of the edge.Comment: 40 pages, 10 figures. v2 added citations, now 41 page
Noise on complex quantum Hall edges: Chiral anomaly and heat diffusion
Electrical and thermal conductances of a quantum Hall bar reflect the
topological structure of the incompressible bulk phase. Here we show that noise
of electrical current carried through the edge evidences the interplay between
these two topological observables. Transport through a structured edge is
modeled by a voltage-biased line junction made up of two counter-propagating
modes associated with respective filling factors. Specifically, we focus on the
edge of a fractional quantum Hall state. Noise is generated at a
point distinctly separated from the hot spot (where most of the Ohmic
dissipation takes place) and reflects the competition between ballistically
carried downstream current and diffusively carried heat (which can propagate
also upstream). We propose specific setups where our predictions can be
measured.Comment: 5pages, 5 figures, 5-page supplemental materia
Macroscopic Quantum Entanglement of a Kondo Cloud at Finite Temperature
We propose a variational approach for computing the macroscopic entanglement
in a many-body mixed state, based on entanglement witness operators, and
compute the entanglement of formation (EoF), a mixed-state generalization of
the entanglement entropy, in single- and two-channel Kondo systems at finite
temperature. The thermal suppression of the EoF obeys power-law scaling at low
temperature. The scaling exponent is halved from the single- to the two-channel
system, which is attributed, using a bosonization method, to the non-Fermi
liquid behavior of a Majorana fermion, a "half" of a complex fermion, emerging
in the two-channel system. Moreover, the EoF characterizes the size and
power-law tail of the Kondo screening cloud of the single-channel system.Comment: Supplementary Material include
Topological vacuum bubble by anyon braiding
According to a basic rule of fermionic and bosonic many-body physics, known
as the linked cluster theorem, physical observables are not affected by vacuum
bubbles, which represent virtual particles created from vacuum and
self-annihilating without interacting with real particles. Here, we show that
this conventional knowledge must be revised for anyons, quasiparticles that
obey fractional exchange statistics intermediate between fermions and bosons.
We find that a certain class of vacuum bubbles of Abelian anyons does affect
physical observables. They represent virtually excited anyons which wind around
real anyonic excitations. These topological bubbles result in a
temperature-dependent phase shift of Fabry-Perot interference patterns in the
fractional quantum Hall regime accessible in current experiments, thus
providing a tool for direct and unambiguous observation of elusive fractional
statistics.Comment: 7 pages, 4 figures, and 9 pages of Supplementary Informatio
Negative- Anisotropic Charge Kondo Effect in a Triple Quantum Dot
We predict a new type of the negative- Anderson impurity formed in a
triple quantum dot. The two dots of the system behave as a negative-
impurity preferring zero or double electron occupancy rather than single
occupancy, and the third dot stabilizes the attractive interaction of
via Coulomb repulsion. Using a bosonization method, we find that the system has
the two different phases of massive or vanishing charge fluctuations between
the two occupancies at low temperature, which are equivalent with the
antiferromagnetic and ferromagnetic phases of the anisotropic Kondo model,
respectively. The phase transition is experimentally accessible and
identifiable by electron conductance, offering the possibility of
experimentally exploring the anisotropic Kondo model
How to directly measure a Kondo cloud's length
We propose a method to directly measure, by electrical means, the Kondo
screening cloud formed by an Anderson impurity coupled to semi-infinite quantum
wires, on which an electrostatic gate voltage is applied at distance L from the
impurity. We show that the Kondo cloud, and hence the Kondo temperature and the
electron conductance through the impurity, are affected by the gate voltage, as
L decreases below the Kondo cloud length. Based on this behavior, the cloud
length can be experimentally identified by changing L with a keyboard type of
gate voltage or tuning the coupling strength between the impurity and the
wires.Comment: 5 pages, 4 figure
Anisotropic charge Kondo effect in a triple quantum dot
We predict that an anisotropic charge Kondo effect appears in a triple
quantum dot, when the system has two-fold degenerate ground states of (1,1,0)
and (0,0,1) charge configurations. Using bosonization and refermionization
methods, we find that at low temperature, the system has the two different
phases of massive charge fluctuations between the two charge configurations and
vanishing fluctuations, which are equivalent with the Kondo-screened and
ferromagnetic phases of the anisotropic Kondo model, respectively. The phase
transition is identifiable by electron conductance measurement, offering the
possibility of experimentally exploring the anisotropic Kondo model. Our charge
Kondo effect has similar origin to that in a negative-U Anderson impurity.Comment: 5 pages, 2 figure
Symmetry-related transport on a fractional quantum Hall edge
Low-energy transport in quantum Hall states is carried through edge modes,
and is dictated by bulk topological invariants and possibly microscopic
Boltzmann kinetics at the edge. Here we show how the presence or breaking of
symmetries of the edge Hamiltonian underlie transport properties, specifically
d.c. conductance and noise. We demonstrate this through the analysis of
hole-conjugate states of the quantum Hall effect, specifically the
case in a quantum point-contact (QPC) geometry. We identify two symmetries, a
continuous and a discrete , whose presence or absence (different
symmetry scenarios) dictate qualitatively different types of behavior of
conductance and shot noise. While recent measurements are consistent with one
of these symmetry scenarios, others can be realized in future experiments.Comment: 14 pages, 6 figure
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